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Runge-Kutta 4th Order with 1 State Variable1 Change only the colored cells.

equation: y'=y Control+e to extract data for graph.

dt y_00.01 1

n t y yp0 0 1 1

0 1 10 1 1

0.01 1.01 1.011 0.01 1.01 1.01

0.01 1.01 1.010.01 1.01 1.010.01 1.01 1.01

2 0.01 1.01 1.010.01 1.01 1.01

0.01 1.01 1.010.02 1.02 1.02

3 0.02 1.02 1.020.02 1.02 1.020.02 1.02 1.020.02 1.02 1.02

4 0.02 1.02 1.020.02 1.02 1.020.02 1.02 1.020.03 1.03 1.03

5 0.03 1.03 1.030.03 1.03 1.03

0.03 1.03 1.030.03 1.03 1.03

6 0.03 1.03 1.030.03 1.03 1.030.03 1.03 1.030.04 1.04 1.04

7 0.04 1.04 1.040.04 1.04 1.040.04 1.04 1.040.04 1.04 1.04

8 0.04 1.04 1.040.04 1.04 1.04

0.04 1.04 1.040.05 1.05 1.05

9 0.05 1.05 1.050.05 1.05 1.050.05 1.05 1.050.05 1.05 1.05

10 0.05 1.05 1.050.05 1.05 1.050.05 1.05 1.05

0 0.5

0

2

4

6

8

10

12

14

put

y

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0.06 1.06 1.0611 0.06 1.06 1.06

0.06 1.06 1.060.06 1.06 1.060.06 1.06 1.06

12 0.06 1.06 1.06

0.06 1.06 1.060.06 1.06 1.060.06 1.07 1.07

13 0.06 1.07 1.070.07 1.07 1.070.07 1.07 1.070.07 1.07 1.07

14 0.07 1.07 1.070.07 1.08 1.080.07 1.08 1.080.08 1.08 1.08

15 0.08 1.08 1.08

0.08 1.08 1.080.08 1.08 1.080.08 1.08 1.08

16 0.08 1.08 1.080.08 1.09 1.090.08 1.09 1.090.09 1.09 1.09

17 0.09 1.09 1.090.09 1.09 1.090.09 1.09 1.090.09 1.09 1.09

18 0.09 1.09 1.09

0.09 1.1 1.10.09 1.1 1.1

0.1 1.1 1.119 0.1 1.1 1.1

0.1 1.1 1.10.1 1.1 1.10.1 1.11 1.11

20 0.1 1.11 1.110.1 1.11 1.110.1 1.11 1.11

0.11 1.11 1.1121 0.11 1.11 1.11

0.11 1.11 1.110.11 1.11 1.110.11 1.12 1.12

22 0.11 1.12 1.120.11 1.12 1.120.11 1.12 1.120.12 1.12 1.12

23 0.12 1.12 1.120.12 1.12 1.12

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0.12 1.12 1.120.12 1.13 1.13

24 0.12 1.13 1.130.12 1.13 1.130.12 1.13 1.130.13 1.13 1.13

25 0.13 1.13 1.130.13 1.14 1.140.13 1.14 1.140.13 1.14 1.14

26 0.13 1.14 1.140.13 1.14 1.140.13 1.14 1.140.14 1.14 1.14

27 0.14 1.14 1.140.14 1.15 1.150.14 1.15 1.150.14 1.15 1.15

28 0.14 1.15 1.150.14 1.15 1.150.14 1.15 1.150.15 1.16 1.16

29 0.15 1.16 1.160.15 1.16 1.160.15 1.16 1.160.15 1.16 1.16

30 0.15 1.16 1.160.15 1.16 1.160.15 1.16 1.160.16 1.17 1.17

31 0.16 1.17 1.170.16 1.17 1.170.16 1.17 1.170.16 1.17 1.17

32 0.16 1.17 1.170.16 1.18 1.180.16 1.18 1.180.17 1.18 1.18

33 0.17 1.18 1.180.17 1.18 1.180.17 1.18 1.180.17 1.19 1.19

34 0.17 1.19 1.190.17 1.19 1.190.17 1.19 1.190.18 1.19 1.19

35 0.18 1.19 1.190.18 1.19 1.190.18 1.19 1.190.18 1.2 1.2

36 0.18 1.2 1.2

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0.18 1.2 1.20.18 1.2 1.20.19 1.2 1.2

37 0.19 1.2 1.20.19 1.21 1.210.19 1.21 1.21

0.19 1.21 1.2138 0.19 1.21 1.21

0.19 1.21 1.210.19 1.21 1.21

0.2 1.22 1.2239 0.2 1.22 1.22

0.2 1.22 1.220.2 1.22 1.220.2 1.22 1.22

40 0.2 1.22 1.220.2 1.22 1.220.2 1.22 1.22

0.21 1.23 1.2341 0.21 1.23 1.23

0.21 1.23 1.230.21 1.23 1.230.21 1.23 1.23

42 0.21 1.23 1.230.21 1.24 1.240.21 1.24 1.240.22 1.24 1.24

43 0.22 1.24 1.240.22 1.24 1.240.22 1.24 1.24

0.22 1.25 1.2544 0.22 1.25 1.25

0.22 1.25 1.250.22 1.25 1.250.23 1.25 1.25

45 0.23 1.25 1.250.23 1.26 1.260.23 1.26 1.260.23 1.26 1.26

46 0.23 1.26 1.260.23 1.26 1.260.23 1.26 1.26

0.24 1.26 1.2647 0.24 1.26 1.26

0.24 1.27 1.270.24 1.27 1.270.24 1.27 1.27

48 0.24 1.27 1.270.24 1.27 1.270.24 1.27 1.270.25 1.28 1.28

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49 0.25 1.28 1.280.25 1.28 1.280.25 1.28 1.280.25 1.28 1.28

50 0.25 1.28 1.280.25 1.29 1.29

0.25 1.29 1.290.26 1.29 1.29

51 0.26 1.29 1.290.26 1.29 1.290.26 1.29 1.290.26 1.3 1.3

52 0.26 1.3 1.30.26 1.3 1.30.26 1.3 1.30.27 1.3 1.3

53 0.27 1.3 1.30.27 1.31 1.31

0.27 1.31 1.310.27 1.31 1.31

54 0.27 1.31 1.310.27 1.31 1.310.27 1.31 1.310.28 1.32 1.32

55 0.28 1.32 1.320.28 1.32 1.320.28 1.32 1.320.28 1.32 1.32

56 0.28 1.32 1.320.28 1.33 1.33

0.28 1.33 1.330.29 1.33 1.33

57 0.29 1.33 1.330.29 1.33 1.330.29 1.33 1.330.29 1.34 1.34

58 0.29 1.34 1.340.29 1.34 1.340.29 1.34 1.34

0.3 1.34 1.3459 0.3 1.34 1.34

0.3 1.35 1.35

0.3 1.35 1.350.3 1.35 1.35

60 0.3 1.35 1.350.3 1.35 1.350.3 1.35 1.35

0.31 1.36 1.3661 0.31 1.36 1.36

0.31 1.36 1.360.31 1.36 1.36

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0.31 1.36 1.3662 0.31 1.36 1.36

0.31 1.37 1.370.31 1.37 1.370.32 1.37 1.37

63 0.32 1.37 1.37

0.32 1.37 1.370.32 1.37 1.370.32 1.38 1.38

64 0.32 1.38 1.380.32 1.38 1.380.32 1.38 1.380.33 1.38 1.38

65 0.33 1.38 1.380.33 1.39 1.390.33 1.39 1.390.33 1.39 1.39

66 0.33 1.39 1.39

0.33 1.39 1.390.33 1.39 1.390.34 1.4 1.4

67 0.34 1.4 1.40.34 1.4 1.40.34 1.4 1.40.34 1.4 1.4

68 0.34 1.4 1.40.34 1.41 1.410.34 1.41 1.410.35 1.41 1.41

69 0.35 1.41 1.41

0.35 1.42 1.420.35 1.42 1.420.35 1.42 1.42

70 0.35 1.42 1.420.35 1.42 1.420.35 1.42 1.420.36 1.43 1.43

71 0.36 1.43 1.430.36 1.43 1.430.36 1.43 1.430.36 1.43 1.43

72 0.36 1.43 1.43

0.36 1.44 1.440.36 1.44 1.440.37 1.44 1.44

73 0.37 1.44 1.440.37 1.44 1.440.37 1.44 1.440.37 1.45 1.45

74 0.37 1.45 1.450.37 1.45 1.45

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0.37 1.45 1.450.38 1.45 1.45

75 0.38 1.45 1.450.38 1.46 1.460.38 1.46 1.460.38 1.46 1.46

76 0.38 1.46 1.460.38 1.47 1.470.38 1.47 1.470.39 1.47 1.47

77 0.39 1.47 1.470.39 1.47 1.470.39 1.47 1.470.39 1.48 1.48

78 0.39 1.48 1.480.39 1.48 1.480.39 1.48 1.48

0.4 1.48 1.48

79 0.4 1.48 1.480.4 1.49 1.490.4 1.49 1.490.4 1.49 1.49

80 0.4 1.49 1.490.4 1.5 1.50.4 1.5 1.5

0.41 1.5 1.581 0.41 1.5 1.5

0.41 1.5 1.50.41 1.5 1.50.41 1.51 1.51

82 0.41 1.51 1.510.41 1.51 1.510.41 1.51 1.510.42 1.51 1.51

83 0.42 1.51 1.510.42 1.52 1.520.42 1.52 1.520.42 1.52 1.52

84 0.42 1.52 1.520.42 1.53 1.530.42 1.53 1.530.43 1.53 1.53

85 0.43 1.53 1.530.43 1.53 1.530.43 1.53 1.530.43 1.54 1.54

86 0.43 1.54 1.540.43 1.54 1.540.43 1.54 1.540.44 1.54 1.54

87 0.44 1.54 1.54

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0.44 1.55 1.550.44 1.55 1.550.44 1.55 1.55

88 0.44 1.55 1.550.44 1.56 1.560.44 1.56 1.56

0.45 1.56 1.5689 0.45 1.56 1.56

0.45 1.56 1.560.45 1.56 1.560.45 1.57 1.57

90 0.45 1.57 1.570.45 1.57 1.570.45 1.57 1.570.46 1.58 1.58

91 0.46 1.58 1.580.46 1.58 1.580.46 1.58 1.58

0.46 1.58 1.5892 0.46 1.58 1.58

0.46 1.59 1.590.46 1.59 1.590.47 1.59 1.59

93 0.47 1.59 1.590.47 1.6 1.60.47 1.6 1.60.47 1.6 1.6

94 0.47 1.6 1.60.47 1.6 1.60.47 1.6 1.6

0.48 1.61 1.6195 0.48 1.61 1.61

0.48 1.61 1.610.48 1.61 1.610.48 1.62 1.62

96 0.48 1.62 1.620.48 1.62 1.620.48 1.62 1.620.49 1.62 1.62

97 0.49 1.62 1.620.49 1.63 1.630.49 1.63 1.63

0.49 1.63 1.6398 0.49 1.63 1.63

0.49 1.64 1.640.49 1.64 1.64

0.5 1.64 1.6499 0.5 1.64 1.64

0.5 1.64 1.640.5 1.64 1.640.5 1.65 1.65

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100 0.5 1.65 1.650.5 1.65 1.650.5 1.65 1.65

0.51 1.66 1.66101 0.51 1.66 1.66

0.51 1.66 1.66

0.51 1.66 1.660.51 1.67 1.67

102 0.51 1.67 1.670.51 1.67 1.670.51 1.67 1.670.52 1.67 1.67

103 0.52 1.67 1.670.52 1.68 1.680.52 1.68 1.680.52 1.68 1.68

104 0.52 1.68 1.680.52 1.69 1.69

0.52 1.69 1.690.53 1.69 1.69

105 0.53 1.69 1.690.53 1.69 1.690.53 1.69 1.690.53 1.7 1.7

106 0.53 1.7 1.70.53 1.7 1.70.53 1.7 1.70.54 1.71 1.71

107 0.54 1.71 1.710.54 1.71 1.71

0.54 1.71 1.710.54 1.72 1.72

108 0.54 1.72 1.720.54 1.72 1.720.54 1.72 1.720.55 1.72 1.72

109 0.55 1.72 1.720.55 1.73 1.730.55 1.73 1.730.55 1.73 1.73

110 0.55 1.73 1.730.55 1.74 1.74

0.55 1.74 1.740.56 1.74 1.74

111 0.56 1.74 1.740.56 1.75 1.750.56 1.75 1.750.56 1.75 1.75

112 0.56 1.75 1.750.56 1.76 1.760.56 1.76 1.76

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0.57 1.76 1.76113 0.57 1.76 1.76

0.57 1.76 1.760.57 1.76 1.760.57 1.77 1.77

114 0.57 1.77 1.77

0.57 1.77 1.770.57 1.77 1.770.58 1.78 1.78

115 0.58 1.78 1.780.58 1.78 1.780.58 1.78 1.780.58 1.79 1.79

116 0.58 1.79 1.790.58 1.79 1.790.58 1.79 1.790.59 1.79 1.79

117 0.59 1.79 1.79

0.59 1.8 1.80.59 1.8 1.80.59 1.8 1.8

118 0.59 1.8 1.80.59 1.81 1.810.59 1.81 1.81

0.6 1.81 1.81119 0.6 1.81 1.81

0.6 1.82 1.820.6 1.82 1.820.6 1.82 1.82

120 0.6 1.82 1.82

0.6 1.83 1.830.6 1.83 1.83

0.61 1.83 1.83121 0.61 1.83 1.83

0.61 1.84 1.840.61 1.84 1.840.61 1.84 1.84

122 0.61 1.84 1.840.61 1.85 1.850.61 1.85 1.850.62 1.85 1.85

123 0.62 1.85 1.85

0.62 1.85 1.850.62 1.85 1.850.62 1.86 1.86

124 0.62 1.86 1.860.62 1.86 1.860.62 1.86 1.860.63 1.87 1.87

125 0.63 1.87 1.870.63 1.87 1.87

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0.63 1.87 1.870.63 1.88 1.88

126 0.63 1.88 1.880.63 1.88 1.880.63 1.88 1.880.64 1.89 1.89

127 0.64 1.89 1.890.64 1.89 1.890.64 1.89 1.890.64 1.9 1.9

128 0.64 1.9 1.90.64 1.9 1.90.64 1.9 1.90.65 1.91 1.91

129 0.65 1.91 1.910.65 1.91 1.910.65 1.91 1.910.65 1.92 1.92

130 0.65 1.92 1.920.65 1.92 1.920.65 1.92 1.920.66 1.93 1.93

131 0.66 1.93 1.930.66 1.93 1.930.66 1.93 1.930.66 1.93 1.93

132 0.66 1.93 1.930.66 1.94 1.940.66 1.94 1.940.67 1.94 1.94

133 0.67 1.94 1.940.67 1.95 1.950.67 1.95 1.950.67 1.95 1.95

134 0.67 1.95 1.950.67 1.96 1.960.67 1.96 1.960.68 1.96 1.96

135 0.68 1.96 1.960.68 1.97 1.970.68 1.97 1.970.68 1.97 1.97

136 0.68 1.97 1.970.68 1.98 1.980.68 1.98 1.980.69 1.98 1.98

137 0.69 1.98 1.980.69 1.99 1.990.69 1.99 1.990.69 1.99 1.99

138 0.69 1.99 1.99

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0.69 2 20.69 2 2

0.7 2 2139 0.7 2 2

0.7 2.01 2.010.7 2.01 2.01

0.7 2.01 2.01140 0.7 2.01 2.01

0.7 2.02 2.020.7 2.02 2.02

0.71 2.02 2.02141 0.71 2.02 2.02

0.71 2.03 2.030.71 2.03 2.030.71 2.03 2.03

142 0.71 2.03 2.030.71 2.04 2.040.71 2.04 2.04

0.72 2.04 2.04143 0.72 2.04 2.04

0.72 2.05 2.050.72 2.05 2.050.72 2.05 2.05

144 0.72 2.05 2.050.72 2.06 2.060.72 2.06 2.060.73 2.06 2.06

145 0.73 2.06 2.060.73 2.07 2.070.73 2.07 2.07

0.73 2.08 2.08146 0.73 2.08 2.08

0.73 2.08 2.080.73 2.08 2.080.74 2.09 2.09

147 0.74 2.09 2.090.74 2.09 2.090.74 2.09 2.090.74 2.1 2.1

148 0.74 2.1 2.10.74 2.1 2.10.74 2.1 2.1

0.75 2.11 2.11149 0.75 2.11 2.11

0.75 2.11 2.110.75 2.11 2.110.75 2.12 2.12

150 0.75 2.12 2.120.75 2.12 2.120.75 2.12 2.120.76 2.13 2.13

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151 0.76 2.13 2.130.76 2.13 2.130.76 2.13 2.130.76 2.14 2.14

152 0.76 2.14 2.140.76 2.14 2.14

0.76 2.14 2.140.77 2.15 2.15

153 0.77 2.15 2.150.77 2.15 2.150.77 2.15 2.150.77 2.16 2.16

154 0.77 2.16 2.160.77 2.17 2.170.77 2.17 2.170.78 2.17 2.17

155 0.78 2.17 2.170.78 2.18 2.18

0.78 2.18 2.180.78 2.18 2.18

156 0.78 2.18 2.180.78 2.19 2.190.78 2.19 2.190.79 2.19 2.19

157 0.79 2.19 2.190.79 2.2 2.20.79 2.2 2.20.79 2.2 2.2

158 0.79 2.2 2.20.79 2.21 2.21

0.79 2.21 2.210.8 2.21 2.21

159 0.8 2.21 2.210.8 2.22 2.220.8 2.22 2.220.8 2.23 2.23

160 0.8 2.23 2.230.8 2.23 2.230.8 2.23 2.23

0.81 2.24 2.24161 0.81 2.24 2.24

0.81 2.24 2.24

0.81 2.24 2.240.81 2.25 2.25

162 0.81 2.25 2.250.81 2.25 2.250.81 2.25 2.250.82 2.26 2.26

163 0.82 2.26 2.260.82 2.26 2.260.82 2.26 2.26

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0.82 2.27 2.27164 0.82 2.27 2.27

0.82 2.28 2.280.82 2.28 2.280.83 2.28 2.28

165 0.83 2.28 2.28

0.83 2.29 2.290.83 2.29 2.290.83 2.29 2.29

166 0.83 2.29 2.290.83 2.3 2.30.83 2.3 2.30.84 2.3 2.3

167 0.84 2.3 2.30.84 2.31 2.310.84 2.31 2.310.84 2.32 2.32

168 0.84 2.32 2.32

0.84 2.32 2.320.84 2.32 2.320.85 2.33 2.33

169 0.85 2.33 2.330.85 2.33 2.330.85 2.33 2.330.85 2.34 2.34

170 0.85 2.34 2.340.85 2.35 2.350.85 2.35 2.350.86 2.35 2.35

171 0.86 2.35 2.35

0.86 2.36 2.360.86 2.36 2.360.86 2.36 2.36

172 0.86 2.36 2.360.86 2.37 2.370.86 2.37 2.370.87 2.38 2.38

173 0.87 2.38 2.380.87 2.38 2.380.87 2.38 2.380.87 2.39 2.39

174 0.87 2.39 2.39

0.87 2.39 2.390.87 2.39 2.390.88 2.4 2.4

175 0.88 2.4 2.40.88 2.4 2.40.88 2.4 2.40.88 2.41 2.41

176 0.88 2.41 2.410.88 2.42 2.42

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0.88 2.42 2.420.89 2.42 2.42

177 0.89 2.42 2.420.89 2.43 2.430.89 2.43 2.430.89 2.44 2.44

178 0.89 2.44 2.440.89 2.44 2.440.89 2.44 2.44

0.9 2.45 2.45179 0.9 2.45 2.45

0.9 2.45 2.450.9 2.45 2.450.9 2.46 2.46

180 0.9 2.46 2.460.9 2.47 2.470.9 2.47 2.47

0.91 2.47 2.47

181 0.91 2.47 2.470.91 2.48 2.480.91 2.48 2.480.91 2.48 2.48

182 0.91 2.48 2.480.91 2.49 2.490.91 2.49 2.490.92 2.5 2.5

183 0.92 2.5 2.50.92 2.5 2.50.92 2.5 2.50.92 2.51 2.51

184 0.92 2.51 2.510.92 2.52 2.520.92 2.52 2.520.93 2.52 2.52

185 0.93 2.52 2.520.93 2.53 2.530.93 2.53 2.530.93 2.53 2.53

186 0.93 2.53 2.530.93 2.54 2.540.93 2.54 2.540.94 2.55 2.55

187 0.94 2.55 2.550.94 2.55 2.550.94 2.55 2.550.94 2.56 2.56

188 0.94 2.56 2.560.94 2.57 2.570.94 2.57 2.570.95 2.57 2.57

189 0.95 2.57 2.57

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0.95 2.58 2.580.95 2.58 2.580.95 2.59 2.59

190 0.95 2.59 2.590.95 2.59 2.590.95 2.59 2.59

0.96 2.6 2.6191 0.96 2.6 2.6

0.96 2.61 2.610.96 2.61 2.610.96 2.61 2.61

192 0.96 2.61 2.610.96 2.62 2.620.96 2.62 2.620.97 2.62 2.62

193 0.97 2.62 2.620.97 2.63 2.630.97 2.63 2.63

0.97 2.64 2.64194 0.97 2.64 2.64

0.97 2.64 2.640.97 2.64 2.640.98 2.65 2.65

195 0.98 2.65 2.650.98 2.66 2.660.98 2.66 2.660.98 2.66 2.66

196 0.98 2.66 2.660.98 2.67 2.670.98 2.67 2.67

0.99 2.68 2.68197 0.99 2.68 2.68

0.99 2.68 2.680.99 2.68 2.680.99 2.69 2.69

198 0.99 2.69 2.690.99 2.7 2.70.99 2.7 2.7

1 2.7 2.7199 1 2.7 2.7

1 2.71 2.711 2.71 2.71

1 2.72 2.72200 1 2.72 2.72

1 2.73 2.731 2.73 2.73

1.01 2.73 2.73201 1.01 2.73 2.73

1.01 2.74 2.741.01 2.74 2.741.01 2.75 2.75

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202 1.01 2.75 2.751.01 2.75 2.751.01 2.75 2.751.02 2.76 2.76

203 1.02 2.76 2.761.02 2.77 2.77

1.02 2.77 2.771.02 2.77 2.77

204 1.02 2.77 2.771.02 2.78 2.781.02 2.78 2.781.03 2.79 2.79

205 1.03 2.79 2.791.03 2.79 2.791.03 2.79 2.791.03 2.8 2.8

206 1.03 2.8 2.81.03 2.81 2.81

1.03 2.81 2.811.04 2.82 2.82

207 1.04 2.82 2.821.04 2.82 2.821.04 2.82 2.821.04 2.83 2.83

208 1.04 2.83 2.831.04 2.84 2.841.04 2.84 2.841.05 2.84 2.84

209 1.05 2.84 2.841.05 2.85 2.85

1.05 2.85 2.851.05 2.86 2.86

210 1.05 2.86 2.861.05 2.86 2.861.05 2.86 2.861.06 2.87 2.87

211 1.06 2.87 2.871.06 2.88 2.881.06 2.88 2.881.06 2.89 2.89

212 1.06 2.89 2.891.06 2.89 2.89

1.06 2.89 2.891.07 2.9 2.9

213 1.07 2.9 2.91.07 2.91 2.911.07 2.91 2.911.07 2.92 2.92

214 1.07 2.92 2.921.07 2.92 2.921.07 2.92 2.92

8/6/2019 rk4d1

18/91

1.08 2.93 2.93215 1.08 2.93 2.93

1.08 2.94 2.941.08 2.94 2.941.08 2.94 2.94

216 1.08 2.94 2.94

1.08 2.95 2.951.08 2.95 2.951.09 2.96 2.96

217 1.09 2.96 2.961.09 2.97 2.971.09 2.97 2.971.09 2.97 2.97

218 1.09 2.97 2.971.09 2.98 2.981.09 2.98 2.98

1.1 2.99 2.99219 1.1 2.99 2.99

1.1 3 31.1 3 31.1 3 3

220 1.1 3 31.1 3.01 3.011.1 3.01 3.01

1.11 3.02 3.02221 1.11 3.02 3.02

1.11 3.03 3.031.11 3.03 3.031.11 3.03 3.03

222 1.11 3.03 3.03

1.11 3.04 3.041.11 3.04 3.041.12 3.05 3.05

223 1.12 3.05 3.051.12 3.06 3.061.12 3.06 3.061.12 3.06 3.06

224 1.12 3.06 3.061.12 3.07 3.071.12 3.07 3.071.13 3.08 3.08

225 1.13 3.08 3.08

1.13 3.09 3.091.13 3.09 3.091.13 3.1 3.1

226 1.13 3.1 3.11.13 3.1 3.11.13 3.1 3.11.14 3.11 3.11

227 1.14 3.11 3.111.14 3.12 3.12

8/6/2019 rk4d1

19/91

1.14 3.12 3.121.14 3.13 3.13

228 1.14 3.13 3.131.14 3.13 3.131.14 3.13 3.131.15 3.14 3.14

229 1.15 3.14 3.141.15 3.15 3.151.15 3.15 3.151.15 3.16 3.16

230 1.15 3.16 3.161.15 3.17 3.171.15 3.17 3.171.16 3.17 3.17

231 1.16 3.17 3.171.16 3.18 3.181.16 3.18 3.181.16 3.19 3.19

232 1.16 3.19 3.191.16 3.2 3.21.16 3.2 3.21.17 3.21 3.21

233 1.17 3.21 3.211.17 3.21 3.211.17 3.21 3.211.17 3.22 3.22

234 1.17 3.22 3.221.17 3.23 3.231.17 3.23 3.231.18 3.24 3.24

235 1.18 3.24 3.241.18 3.25 3.251.18 3.25 3.251.18 3.25 3.25

236 1.18 3.25 3.251.18 3.26 3.261.18 3.26 3.261.19 3.27 3.27

237 1.19 3.27 3.271.19 3.28 3.281.19 3.28 3.281.19 3.29 3.29

238 1.19 3.29 3.291.19 3.3 3.31.19 3.3 3.3

1.2 3.3 3.3239 1.2 3.3 3.3

1.2 3.31 3.311.2 3.31 3.311.2 3.32 3.32

240 1.2 3.32 3.32

8/6/2019 rk4d1

20/91

1.2 3.33 3.331.2 3.33 3.33

1.21 3.34 3.34241 1.21 3.34 3.34

1.21 3.35 3.351.21 3.35 3.35

1.21 3.35 3.35242 1.21 3.35 3.35

1.21 3.36 3.361.21 3.36 3.361.22 3.37 3.37

243 1.22 3.37 3.371.22 3.38 3.381.22 3.38 3.381.22 3.39 3.39

244 1.22 3.39 3.391.22 3.4 3.41.22 3.4 3.4

1.23 3.4 3.4245 1.23 3.4 3.4

1.23 3.41 3.411.23 3.41 3.411.23 3.42 3.42

246 1.23 3.42 3.421.23 3.43 3.431.23 3.43 3.431.24 3.44 3.44

247 1.24 3.44 3.441.24 3.45 3.451.24 3.45 3.45

1.24 3.46 3.46248 1.24 3.46 3.46

1.24 3.46 3.461.24 3.46 3.461.25 3.47 3.47

249 1.25 3.47 3.471.25 3.48 3.481.25 3.48 3.481.25 3.49 3.49

250 1.25 3.49 3.491.25 3.5 3.51.25 3.5 3.5

1.26 3.51 3.51251 1.26 3.51 3.51

1.26 3.52 3.521.26 3.52 3.521.26 3.53 3.53

252 1.26 3.53 3.531.26 3.53 3.531.26 3.53 3.531.27 3.54 3.54

8/6/2019 rk4d1

21/91

253 1.27 3.54 3.541.27 3.55 3.551.27 3.55 3.551.27 3.56 3.56

254 1.27 3.56 3.561.27 3.57 3.57

1.27 3.57 3.571.28 3.58 3.58

255 1.28 3.58 3.581.28 3.59 3.591.28 3.59 3.591.28 3.6 3.6

256 1.28 3.6 3.61.28 3.61 3.611.28 3.61 3.611.29 3.61 3.61

257 1.29 3.61 3.611.29 3.62 3.62

1.29 3.62 3.621.29 3.63 3.63

258 1.29 3.63 3.631.29 3.64 3.641.29 3.64 3.64

1.3 3.65 3.65259 1.3 3.65 3.65

1.3 3.66 3.661.3 3.66 3.661.3 3.67 3.67

260 1.3 3.67 3.671.3 3.68 3.68

1.3 3.68 3.681.31 3.69 3.69

261 1.31 3.69 3.691.31 3.7 3.71.31 3.7 3.71.31 3.71 3.71

262 1.31 3.71 3.711.31 3.72 3.721.31 3.72 3.721.32 3.72 3.72

263 1.32 3.72 3.721.32 3.73 3.73

1.32 3.73 3.731.32 3.74 3.74

264 1.32 3.74 3.741.32 3.75 3.751.32 3.75 3.751.33 3.76 3.76

265 1.33 3.76 3.761.33 3.77 3.771.33 3.77 3.77

8/6/2019 rk4d1

22/91

1.33 3.78 3.78266 1.33 3.78 3.78

1.33 3.79 3.791.33 3.79 3.791.34 3.8 3.8

267 1.34 3.8 3.8

1.34 3.81 3.811.34 3.81 3.811.34 3.82 3.82

268 1.34 3.82 3.821.34 3.83 3.831.34 3.83 3.831.35 3.84 3.84

269 1.35 3.84 3.841.35 3.85 3.851.35 3.85 3.851.35 3.86 3.86

270 1.35 3.86 3.86

1.35 3.87 3.871.35 3.87 3.871.36 3.88 3.88

271 1.36 3.88 3.881.36 3.89 3.891.36 3.89 3.891.36 3.9 3.9

272 1.36 3.9 3.91.36 3.91 3.911.36 3.91 3.911.37 3.92 3.92

273 1.37 3.92 3.92

1.37 3.93 3.931.37 3.93 3.931.37 3.94 3.94

274 1.37 3.94 3.941.37 3.95 3.951.37 3.95 3.951.38 3.96 3.96

275 1.38 3.96 3.961.38 3.96 3.961.38 3.96 3.961.38 3.97 3.97

276 1.38 3.97 3.97

1.38 3.98 3.981.38 3.98 3.981.39 3.99 3.99

277 1.39 3.99 3.991.39 4 41.39 4 41.39 4.01 4.01

278 1.39 4.01 4.011.39 4.02 4.02

8/6/2019 rk4d1

23/91

1.39 4.02 4.021.4 4.03 4.03

279 1.4 4.03 4.031.4 4.05 4.051.4 4.05 4.051.4 4.06 4.06

280 1.4 4.06 4.061.4 4.07 4.071.4 4.07 4.07

1.41 4.08 4.08281 1.41 4.08 4.08

1.41 4.09 4.091.41 4.09 4.091.41 4.1 4.1

282 1.41 4.1 4.11.41 4.11 4.111.41 4.11 4.111.42 4.12 4.12

283 1.42 4.12 4.121.42 4.13 4.131.42 4.13 4.131.42 4.14 4.14

284 1.42 4.14 4.141.42 4.15 4.151.42 4.15 4.151.43 4.16 4.16

285 1.43 4.16 4.161.43 4.17 4.171.43 4.17 4.171.43 4.18 4.18

286 1.43 4.18 4.181.43 4.19 4.191.43 4.19 4.191.44 4.2 4.2

287 1.44 4.2 4.21.44 4.21 4.211.44 4.21 4.211.44 4.22 4.22

288 1.44 4.22 4.221.44 4.23 4.231.44 4.23 4.231.45 4.24 4.24

289 1.45 4.24 4.241.45 4.25 4.251.45 4.25 4.251.45 4.26 4.26

290 1.45 4.26 4.261.45 4.27 4.271.45 4.27 4.271.45 4.28 4.28

291 1.45 4.28 4.28

8/6/2019 rk4d1

24/91

1.46 4.3 4.31.46 4.3 4.31.46 4.31 4.31

292 1.46 4.31 4.311.46 4.32 4.321.46 4.32 4.32

1.46 4.33 4.33293 1.46 4.33 4.33

1.47 4.34 4.341.47 4.34 4.341.47 4.35 4.35

294 1.47 4.35 4.351.47 4.36 4.361.47 4.36 4.361.47 4.37 4.37

295 1.47 4.37 4.371.48 4.38 4.381.48 4.38 4.38

1.48 4.39 4.39296 1.48 4.39 4.39

1.48 4.4 4.41.48 4.4 4.41.48 4.41 4.41

297 1.48 4.41 4.411.49 4.43 4.431.49 4.43 4.431.49 4.44 4.44

298 1.49 4.44 4.441.49 4.45 4.451.49 4.45 4.45

1.49 4.46 4.46299 1.49 4.46 4.46

1.5 4.47 4.471.5 4.47 4.471.5 4.48 4.48

300 1.5 4.48 4.481.5 4.49 4.491.5 4.49 4.491.5 4.5 4.5

301 1.5 4.5 4.51.51 4.52 4.521.51 4.52 4.52

1.51 4.53 4.53302 1.51 4.53 4.53

1.51 4.54 4.541.51 4.54 4.541.51 4.55 4.55

303 1.51 4.55 4.551.52 4.56 4.561.52 4.56 4.561.52 4.57 4.57

8/6/2019 rk4d1

25/91

304 1.52 4.57 4.571.52 4.58 4.581.52 4.58 4.581.52 4.6 4.6

305 1.52 4.6 4.61.53 4.61 4.61

1.53 4.61 4.611.53 4.62 4.62

306 1.53 4.62 4.621.53 4.63 4.631.53 4.63 4.631.53 4.64 4.64

307 1.53 4.64 4.641.54 4.65 4.651.54 4.65 4.651.54 4.66 4.66

308 1.54 4.66 4.661.54 4.68 4.68

1.54 4.68 4.681.54 4.69 4.69

309 1.54 4.69 4.691.55 4.7 4.71.55 4.7 4.71.55 4.71 4.71

310 1.55 4.71 4.711.55 4.72 4.721.55 4.72 4.721.55 4.74 4.74

311 1.55 4.74 4.741.56 4.75 4.75

1.56 4.75 4.751.56 4.76 4.76

312 1.56 4.76 4.761.56 4.77 4.771.56 4.77 4.771.56 4.78 4.78

313 1.56 4.78 4.781.57 4.79 4.791.57 4.79 4.791.57 4.81 4.81

314 1.57 4.81 4.811.57 4.82 4.82

1.57 4.82 4.821.57 4.83 4.83

315 1.57 4.83 4.831.58 4.84 4.841.58 4.84 4.841.58 4.85 4.85

316 1.58 4.85 4.851.58 4.87 4.871.58 4.87 4.87

8/6/2019 rk4d1

26/91

1.58 4.88 4.88317 1.58 4.88 4.88

1.59 4.89 4.891.59 4.89 4.891.59 4.9 4.9

318 1.59 4.9 4.9

1.59 4.92 4.921.59 4.92 4.921.59 4.93 4.93

319 1.59 4.93 4.931.6 4.94 4.941.6 4.94 4.941.6 4.95 4.95

320 1.6 4.95 4.951.6 4.97 4.971.6 4.97 4.971.6 4.98 4.98

321 1.6 4.98 4.98

1.61 4.99 4.991.61 4.99 4.991.61 5 5

322 1.61 5 51.61 5.02 5.021.61 5.02 5.021.61 5.03 5.03

323 1.61 5.03 5.031.62 5.04 5.041.62 5.04 5.041.62 5.05 5.05

324 1.62 5.05 5.05

1.62 5.07 5.071.62 5.07 5.071.62 5.08 5.08

325 1.62 5.08 5.081.63 5.09 5.091.63 5.09 5.091.63 5.1 5.1

326 1.63 5.1 5.11.63 5.12 5.121.63 5.12 5.121.63 5.13 5.13

327 1.63 5.13 5.13

1.64 5.14 5.141.64 5.14 5.141.64 5.16 5.16

328 1.64 5.16 5.161.64 5.17 5.171.64 5.17 5.171.64 5.18 5.18

329 1.64 5.18 5.181.65 5.19 5.19

8/6/2019 rk4d1

27/91

1.65 5.19 5.191.65 5.21 5.21

330 1.65 5.21 5.211.65 5.22 5.221.65 5.22 5.221.65 5.23 5.23

331 1.65 5.23 5.231.66 5.25 5.251.66 5.25 5.251.66 5.26 5.26

332 1.66 5.26 5.261.66 5.27 5.271.66 5.27 5.271.66 5.29 5.29

333 1.66 5.29 5.291.67 5.3 5.31.67 5.3 5.31.67 5.31 5.31

334 1.67 5.31 5.311.67 5.33 5.331.67 5.33 5.331.67 5.34 5.34

335 1.67 5.34 5.341.68 5.35 5.351.68 5.35 5.351.68 5.37 5.37

336 1.68 5.37 5.371.68 5.38 5.381.68 5.38 5.381.68 5.39 5.39

337 1.68 5.39 5.391.69 5.41 5.411.69 5.41 5.411.69 5.42 5.42

338 1.69 5.42 5.421.69 5.43 5.431.69 5.43 5.431.69 5.45 5.45

339 1.69 5.45 5.451.7 5.46 5.461.7 5.46 5.461.7 5.47 5.47

340 1.7 5.47 5.471.7 5.49 5.491.7 5.49 5.491.7 5.5 5.5

341 1.7 5.5 5.51.71 5.52 5.521.71 5.52 5.521.71 5.53 5.53

342 1.71 5.53 5.53

8/6/2019 rk4d1

28/91

1.71 5.54 5.541.71 5.54 5.541.71 5.56 5.56

343 1.71 5.56 5.561.72 5.57 5.571.72 5.57 5.57

1.72 5.58 5.58344 1.72 5.58 5.58

1.72 5.6 5.61.72 5.6 5.61.72 5.61 5.61

345 1.72 5.61 5.611.73 5.63 5.631.73 5.63 5.631.73 5.64 5.64

346 1.73 5.64 5.641.73 5.65 5.651.73 5.65 5.65

1.73 5.67 5.67347 1.73 5.67 5.67

1.74 5.68 5.681.74 5.68 5.681.74 5.7 5.7

348 1.74 5.7 5.71.74 5.71 5.711.74 5.71 5.711.74 5.73 5.73

349 1.74 5.73 5.731.75 5.74 5.741.75 5.74 5.74

1.75 5.75 5.75350 1.75 5.75 5.75

1.75 5.77 5.771.75 5.77 5.771.75 5.78 5.78

351 1.75 5.78 5.781.76 5.8 5.81.76 5.8 5.81.76 5.81 5.81

352 1.76 5.81 5.811.76 5.83 5.831.76 5.83 5.83

1.76 5.84 5.84353 1.76 5.84 5.84

1.77 5.86 5.861.77 5.86 5.861.77 5.87 5.87

354 1.77 5.87 5.871.77 5.89 5.891.77 5.89 5.891.77 5.9 5.9

8/6/2019 rk4d1

29/91

355 1.77 5.9 5.91.78 5.92 5.921.78 5.92 5.921.78 5.93 5.93

356 1.78 5.93 5.931.78 5.94 5.94

1.78 5.94 5.941.78 5.96 5.96

357 1.78 5.96 5.961.79 5.97 5.971.79 5.97 5.971.79 5.99 5.99

358 1.79 5.99 5.991.79 6 61.79 6 61.79 6.02 6.02

359 1.79 6.02 6.021.8 6.03 6.03

1.8 6.03 6.031.8 6.05 6.05

360 1.8 6.05 6.051.8 6.06 6.061.8 6.06 6.061.8 6.08 6.08

361 1.8 6.08 6.081.81 6.1 6.11.81 6.1 6.11.81 6.11 6.11

362 1.81 6.11 6.111.81 6.13 6.13

1.81 6.13 6.131.81 6.14 6.14

363 1.81 6.14 6.141.82 6.16 6.161.82 6.16 6.161.82 6.17 6.17

364 1.82 6.17 6.171.82 6.19 6.191.82 6.19 6.191.82 6.2 6.2

365 1.82 6.2 6.21.83 6.22 6.22

1.83 6.22 6.221.83 6.23 6.23

366 1.83 6.23 6.231.83 6.25 6.251.83 6.25 6.251.83 6.27 6.27

367 1.83 6.27 6.271.84 6.28 6.281.84 6.28 6.28

8/6/2019 rk4d1

30/91

1.84 6.3 6.3368 1.84 6.3 6.3

1.84 6.31 6.311.84 6.31 6.311.84 6.33 6.33

369 1.84 6.33 6.33

1.85 6.34 6.341.85 6.34 6.341.85 6.36 6.36

370 1.85 6.36 6.361.85 6.38 6.381.85 6.38 6.381.85 6.39 6.39

371 1.85 6.39 6.391.86 6.41 6.411.86 6.41 6.411.86 6.42 6.42

372 1.86 6.42 6.42

1.86 6.44 6.441.86 6.44 6.441.86 6.46 6.46

373 1.86 6.46 6.461.87 6.47 6.471.87 6.47 6.471.87 6.49 6.49

374 1.87 6.49 6.491.87 6.5 6.51.87 6.5 6.51.87 6.52 6.52

375 1.87 6.52 6.52

1.88 6.54 6.541.88 6.54 6.541.88 6.55 6.55

376 1.88 6.55 6.551.88 6.57 6.571.88 6.57 6.571.88 6.59 6.59

377 1.88 6.59 6.591.89 6.6 6.61.89 6.6 6.61.89 6.62 6.62

378 1.89 6.62 6.62

1.89 6.64 6.641.89 6.64 6.641.89 6.65 6.65

379 1.89 6.65 6.651.9 6.67 6.671.9 6.67 6.671.9 6.69 6.69

380 1.9 6.69 6.691.9 6.7 6.7

8/6/2019 rk4d1

31/91

1.9 6.7 6.71.9 6.72 6.72

381 1.9 6.72 6.721.91 6.74 6.741.91 6.74 6.741.91 6.75 6.75

382 1.91 6.75 6.751.91 6.77 6.771.91 6.77 6.771.91 6.79 6.79

383 1.91 6.79 6.791.92 6.8 6.81.92 6.8 6.81.92 6.82 6.82

384 1.92 6.82 6.821.92 6.84 6.841.92 6.84 6.841.92 6.86 6.86

385 1.92 6.86 6.861.93 6.87 6.871.93 6.87 6.871.93 6.89 6.89

386 1.93 6.89 6.891.93 6.91 6.911.93 6.91 6.911.93 6.92 6.92

387 1.93 6.92 6.921.94 6.94 6.941.94 6.94 6.941.94 6.96 6.96

388 1.94 6.96 6.961.94 6.98 6.981.94 6.98 6.981.94 6.99 6.99

389 1.94 6.99 6.991.95 7.01 7.011.95 7.01 7.011.95 7.03 7.03

390 1.95 7.03 7.031.95 7.05 7.051.95 7.05 7.051.95 7.06 7.06

391 1.95 7.06 7.061.96 7.08 7.081.96 7.08 7.081.96 7.1 7.1

392 1.96 7.1 7.11.96 7.12 7.121.96 7.12 7.121.96 7.13 7.13

393 1.96 7.13 7.13

8/6/2019 rk4d1

32/91

1.97 7.15 7.151.97 7.15 7.151.97 7.17 7.17

394 1.97 7.17 7.171.97 7.19 7.191.97 7.19 7.19

1.97 7.21 7.21395 1.97 7.21 7.21

1.98 7.22 7.221.98 7.22 7.221.98 7.24 7.24

396 1.98 7.24 7.241.98 7.26 7.261.98 7.26 7.261.98 7.28 7.28

397 1.98 7.28 7.281.99 7.3 7.31.99 7.3 7.3

1.99 7.32 7.32398 1.99 7.32 7.32

1.99 7.33 7.331.99 7.33 7.331.99 7.35 7.35

399 1.99 7.35 7.352 7.37 7.372 7.37 7.372 7.39 7.39

400 2 7.39 7.392 7.41 7.412 7.41 7.41

2 7.43 7.43401 2 7.43 7.43

2.01 7.44 7.442.01 7.44 7.442.01 7.46 7.46

402 2.01 7.46 7.462.01 7.48 7.482.01 7.48 7.482.01 7.5 7.5

403 2.01 7.5 7.52.02 7.52 7.522.02 7.52 7.52

2.02 7.54 7.54404 2.02 7.54 7.54

2.02 7.56 7.562.02 7.56 7.562.02 7.58 7.58

405 2.02 7.58 7.582.03 7.6 7.62.03 7.6 7.62.03 7.61 7.61

8/6/2019 rk4d1

33/91

406 2.03 7.61 7.612.03 7.63 7.632.03 7.63 7.632.03 7.65 7.65

407 2.03 7.65 7.652.04 7.67 7.67

2.04 7.67 7.672.04 7.69 7.69

408 2.04 7.69 7.692.04 7.71 7.712.04 7.71 7.712.04 7.73 7.73

409 2.04 7.73 7.732.05 7.75 7.752.05 7.75 7.752.05 7.77 7.77

410 2.05 7.77 7.772.05 7.79 7.79

2.05 7.79 7.792.05 7.81 7.81

411 2.05 7.81 7.812.06 7.83 7.832.06 7.83 7.832.06 7.85 7.85

412 2.06 7.85 7.852.06 7.87 7.872.06 7.87 7.872.06 7.89 7.89

413 2.06 7.89 7.892.07 7.91 7.91

2.07 7.91 7.912.07 7.92 7.92

414 2.07 7.92 7.922.07 7.94 7.942.07 7.94 7.942.07 7.96 7.96

415 2.07 7.96 7.962.08 7.98 7.982.08 7.98 7.982.08 8 8

416 2.08 8 82.08 8.02 8.02

2.08 8.02 8.022.08 8.04 8.04

417 2.08 8.04 8.042.09 8.06 8.062.09 8.06 8.062.09 8.08 8.08

418 2.09 8.08 8.082.09 8.11 8.112.09 8.11 8.11

8/6/2019 rk4d1

34/91

2.09 8.13 8.13419 2.09 8.13 8.13

2.1 8.15 8.152.1 8.15 8.152.1 8.17 8.17

420 2.1 8.17 8.17

2.1 8.19 8.192.1 8.19 8.192.1 8.21 8.21

421 2.1 8.21 8.212.11 8.23 8.232.11 8.23 8.232.11 8.25 8.25

422 2.11 8.25 8.252.11 8.27 8.272.11 8.27 8.272.11 8.29 8.29

423 2.11 8.29 8.29

2.12 8.31 8.312.12 8.31 8.312.12 8.33 8.33

424 2.12 8.33 8.332.12 8.35 8.352.12 8.35 8.352.12 8.37 8.37

425 2.12 8.37 8.372.13 8.39 8.392.13 8.39 8.392.13 8.41 8.41

426 2.13 8.41 8.41

2.13 8.44 8.442.13 8.44 8.442.13 8.46 8.46

427 2.13 8.46 8.462.14 8.48 8.482.14 8.48 8.482.14 8.5 8.5

428 2.14 8.5 8.52.14 8.52 8.522.14 8.52 8.522.14 8.54 8.54

429 2.14 8.54 8.54

2.15 8.56 8.562.15 8.56 8.562.15 8.58 8.58

430 2.15 8.58 8.582.15 8.61 8.612.15 8.61 8.612.15 8.63 8.63

431 2.15 8.63 8.632.16 8.65 8.65

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2.16 8.65 8.652.16 8.67 8.67

432 2.16 8.67 8.672.16 8.69 8.692.16 8.69 8.692.16 8.71 8.71

433 2.16 8.71 8.712.17 8.74 8.742.17 8.74 8.742.17 8.76 8.76

434 2.17 8.76 8.762.17 8.78 8.782.17 8.78 8.782.17 8.8 8.8

435 2.17 8.8 8.82.18 8.82 8.822.18 8.82 8.822.18 8.85 8.85

436 2.18 8.85 8.852.18 8.87 8.872.18 8.87 8.872.18 8.89 8.89

437 2.18 8.89 8.892.19 8.91 8.912.19 8.91 8.912.19 8.94 8.94

438 2.19 8.94 8.942.19 8.96 8.962.19 8.96 8.962.19 8.98 8.98

439 2.19 8.98 8.982.2 9 92.2 9 92.2 9.03 9.03

440 2.2 9.03 9.032.2 9.05 9.052.2 9.05 9.052.2 9.07 9.07

441 2.2 9.07 9.072.21 9.09 9.092.21 9.09 9.092.21 9.12 9.12

442 2.21 9.12 9.122.21 9.14 9.142.21 9.14 9.142.21 9.16 9.16

443 2.21 9.16 9.162.22 9.18 9.182.22 9.18 9.182.22 9.21 9.21

444 2.22 9.21 9.21

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2.22 9.23 9.232.22 9.23 9.232.22 9.25 9.25

445 2.22 9.25 9.252.23 9.28 9.282.23 9.28 9.28

2.23 9.3 9.3446 2.23 9.3 9.3

2.23 9.32 9.322.23 9.32 9.322.23 9.35 9.35

447 2.23 9.35 9.352.24 9.37 9.372.24 9.37 9.372.24 9.39 9.39

448 2.24 9.39 9.392.24 9.42 9.422.24 9.42 9.42

2.24 9.44 9.44449 2.24 9.44 9.44

2.25 9.46 9.462.25 9.46 9.462.25 9.49 9.49

450 2.25 9.49 9.492.25 9.51 9.512.25 9.51 9.512.25 9.54 9.54

451 2.25 9.54 9.542.26 9.56 9.562.26 9.56 9.56

2.26 9.58 9.58452 2.26 9.58 9.58

2.26 9.61 9.612.26 9.61 9.612.26 9.63 9.63

453 2.26 9.63 9.632.27 9.66 9.662.27 9.66 9.662.27 9.68 9.68

454 2.27 9.68 9.682.27 9.7 9.72.27 9.7 9.7

2.27 9.73 9.73455 2.27 9.73 9.73

2.28 9.75 9.752.28 9.75 9.752.28 9.78 9.78

456 2.28 9.78 9.782.28 9.8 9.82.28 9.8 9.82.28 9.83 9.83

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457 2.28 9.83 9.832.29 9.85 9.852.29 9.85 9.852.29 9.87 9.87

458 2.29 9.87 9.872.29 9.9 9.9

2.29 9.9 9.92.29 9.92 9.92

459 2.29 9.92 9.922.3 9.95 9.952.3 9.95 9.952.3 9.97 9.97

460 2.3 9.97 9.972.3 10 102.3 10 102.3 10.02 10.02

461 2.3 10.02 10.022.31 10.05 10.05

2.31 10.05 10.052.31 10.07 10.07

462 2.31 10.07 10.072.31 10.1 10.12.31 10.1 10.12.31 10.12 10.12

463 2.31 10.12 10.122.32 10.15 10.152.32 10.15 10.152.32 10.18 10.18

464 2.32 10.18 10.182.32 10.2 10.2

2.32 10.2 10.22.32 10.23 10.23

465 2.32 10.23 10.232.33 10.25 10.252.33 10.25 10.252.33 10.28 10.28

466 2.33 10.28 10.282.33 10.3 10.32.33 10.3 10.32.33 10.33 10.33

467 2.33 10.33 10.332.34 10.36 10.36

2.34 10.36 10.362.34 10.38 10.38

468 2.34 10.38 10.382.34 10.41 10.412.34 10.41 10.412.34 10.43 10.43

469 2.34 10.43 10.432.35 10.46 10.462.35 10.46 10.46

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2.35 10.49 10.49470 2.35 10.49 10.49

2.35 10.51 10.512.35 10.51 10.512.35 10.54 10.54

471 2.35 10.54 10.54

2.36 10.56 10.562.36 10.56 10.562.36 10.59 10.59

472 2.36 10.59 10.592.36 10.62 10.622.36 10.62 10.622.36 10.64 10.64

473 2.36 10.64 10.642.37 10.67 10.672.37 10.67 10.672.37 10.7 10.7

474 2.37 10.7 10.7

2.37 10.72 10.722.37 10.72 10.722.37 10.75 10.75

475 2.37 10.75 10.752.38 10.78 10.782.38 10.78 10.782.38 10.8 10.8

476 2.38 10.8 10.82.38 10.83 10.832.38 10.83 10.832.38 10.86 10.86

477 2.38 10.86 10.86

2.39 10.89 10.892.39 10.89 10.892.39 10.91 10.91

478 2.39 10.91 10.912.39 10.94 10.942.39 10.94 10.942.39 10.97 10.97

479 2.39 10.97 10.972.4 11 112.4 11 112.4 11.02 11.02

480 2.4 11.02 11.02

2.4 11.05 11.052.4 11.05 11.052.4 11.08 11.08

481 2.4 11.08 11.082.41 11.11 11.112.41 11.11 11.112.41 11.13 11.13

482 2.41 11.13 11.132.41 11.16 11.16

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2.41 11.16 11.162.41 11.19 11.19

483 2.41 11.19 11.192.42 11.22 11.222.42 11.22 11.222.42 11.25 11.25

484 2.42 11.25 11.252.42 11.27 11.272.42 11.27 11.272.42 11.3 11.3

485 2.42 11.3 11.32.43 11.33 11.332.43 11.33 11.332.43 11.36 11.36

486 2.43 11.36 11.362.43 11.39 11.392.43 11.39 11.392.43 11.42 11.42

487 2.43 11.42 11.422.44 11.44 11.442.44 11.44 11.442.44 11.47 11.47

488 2.44 11.47 11.472.44 11.5 11.52.44 11.5 11.52.44 11.53 11.53

489 2.44 11.53 11.532.45 11.56 11.562.45 11.56 11.562.45 11.59 11.59

490 2.45 11.59 11.592.45 11.62 11.622.45 11.62 11.622.45 11.65 11.65

491 2.45 11.65 11.652.46 11.68 11.682.46 11.68 11.682.46 11.7 11.7

492 2.46 11.7 11.72.46 11.73 11.732.46 11.73 11.732.46 11.76 11.76

493 2.46 11.76 11.762.47 11.79 11.792.47 11.79 11.792.47 11.82 11.82

494 2.47 11.82 11.822.47 11.85 11.852.47 11.85 11.852.47 11.88 11.88

495 2.47 11.88 11.88

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2.48 11.91 11.912.48 11.91 11.912.48 11.94 11.94

496 2.48 11.94 11.942.48 11.97 11.972.48 11.97 11.97

2.48 12 12497 2.48 12 12

2.49 12.03 12.032.49 12.03 12.032.49 12.06 12.06

498 2.49 12.06 12.062.49 12.09 12.092.49 12.09 12.092.49 12.12 12.12

499 2.49 12.12 12.122.5 12.15 12.152.5 12.15 12.15

2.5 12.18 12.18500 2.5 12.18 12.18

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1 1.5 2 2.5 3

quation and init conds here

y

time

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y'=y

filt_critn

>=0

n t y yp0 0 1 11 0.01 1.01 1.012 0.01 1.01 1.013 0.02 1.02 1.024 0.02 1.02 1.025 0.03 1.03 1.036 0.03 1.03 1.037 0.04 1.04 1.048 0.04 1.04 1.049 0.05 1.05 1.05

10 0.05 1.05 1.0511 0.06 1.06 1.0612 0.06 1.06 1.0613 0.07 1.07 1.0714 0.07 1.07 1.0715 0.08 1.08 1.0816 0.08 1.08 1.0817 0.09 1.09 1.0918 0.09 1.09 1.0919 0.1 1.1 1.120 0.1 1.11 1.1121 0.11 1.11 1.11

22 0.11 1.12 1.1223 0.12 1.12 1.1224 0.12 1.13 1.1325 0.13 1.13 1.1326 0.13 1.14 1.1427 0.14 1.14 1.1428 0.14 1.15 1.1529 0.15 1.16 1.1630 0.15 1.16 1.1631 0.16 1.17 1.1732 0.16 1.17 1.1733 0.17 1.18 1.18

34 0.17 1.19 1.1935 0.18 1.19 1.1936 0.18 1.2 1.237 0.19 1.2 1.238 0.19 1.21 1.2139 0.2 1.22 1.2240 0.2 1.22 1.2241 0.21 1.23 1.2342 0.21 1.23 1.23

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43 0.22 1.24 1.2444 0.22 1.25 1.2545 0.23 1.25 1.2546 0.23 1.26 1.2647 0.24 1.26 1.2648 0.24 1.27 1.27

49 0.25 1.28 1.2850 0.25 1.28 1.2851 0.26 1.29 1.2952 0.26 1.3 1.353 0.27 1.3 1.354 0.27 1.31 1.3155 0.28 1.32 1.3256 0.28 1.32 1.3257 0.29 1.33 1.3358 0.29 1.34 1.3459 0.3 1.34 1.3460 0.3 1.35 1.35

61 0.31 1.36 1.3662 0.31 1.36 1.3663 0.32 1.37 1.3764 0.32 1.38 1.3865 0.33 1.38 1.3866 0.33 1.39 1.3967 0.34 1.4 1.468 0.34 1.4 1.469 0.35 1.41 1.4170 0.35 1.42 1.4271 0.36 1.43 1.4372 0.36 1.43 1.43

73 0.37 1.44 1.4474 0.37 1.45 1.4575 0.38 1.45 1.4576 0.38 1.46 1.4677 0.39 1.47 1.4778 0.39 1.48 1.4879 0.4 1.48 1.4880 0.4 1.49 1.4981 0.41 1.5 1.582 0.41 1.51 1.5183 0.42 1.51 1.5184 0.42 1.52 1.52

85 0.43 1.53 1.5386 0.43 1.54 1.5487 0.44 1.54 1.5488 0.44 1.55 1.5589 0.45 1.56 1.5690 0.45 1.57 1.5791 0.46 1.58 1.5892 0.46 1.58 1.5893 0.47 1.59 1.59

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94 0.47 1.6 1.695 0.48 1.61 1.6196 0.48 1.62 1.6297 0.49 1.62 1.6298 0.49 1.63 1.6399 0.5 1.64 1.64

100 0.5 1.65 1.65101 0.51 1.66 1.66102 0.51 1.67 1.67103 0.52 1.67 1.67104 0.52 1.68 1.68105 0.53 1.69 1.69106 0.53 1.7 1.7107 0.54 1.71 1.71108 0.54 1.72 1.72109 0.55 1.72 1.72110 0.55 1.73 1.73111 0.56 1.74 1.74

112 0.56 1.75 1.75113 0.57 1.76 1.76114 0.57 1.77 1.77115 0.58 1.78 1.78116 0.58 1.79 1.79117 0.59 1.79 1.79118 0.59 1.8 1.8119 0.6 1.81 1.81120 0.6 1.82 1.82121 0.61 1.83 1.83122 0.61 1.84 1.84123 0.62 1.85 1.85

124 0.62 1.86 1.86125 0.63 1.87 1.87126 0.63 1.88 1.88127 0.64 1.89 1.89128 0.64 1.9 1.9129 0.65 1.91 1.91130 0.65 1.92 1.92131 0.66 1.93 1.93132 0.66 1.93 1.93133 0.67 1.94 1.94134 0.67 1.95 1.95135 0.68 1.96 1.96

136 0.68 1.97 1.97137 0.69 1.98 1.98138 0.69 1.99 1.99139 0.7 2 2140 0.7 2.01 2.01141 0.71 2.02 2.02142 0.71 2.03 2.03143 0.72 2.04 2.04144 0.72 2.05 2.05

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145 0.73 2.06 2.06146 0.73 2.08 2.08147 0.74 2.09 2.09148 0.74 2.1 2.1149 0.75 2.11 2.11150 0.75 2.12 2.12

151 0.76 2.13 2.13152 0.76 2.14 2.14153 0.77 2.15 2.15154 0.77 2.16 2.16155 0.78 2.17 2.17156 0.78 2.18 2.18157 0.79 2.19 2.19158 0.79 2.2 2.2159 0.8 2.21 2.21160 0.8 2.23 2.23161 0.81 2.24 2.24162 0.81 2.25 2.25

163 0.82 2.26 2.26164 0.82 2.27 2.27165 0.83 2.28 2.28166 0.83 2.29 2.29167 0.84 2.3 2.3168 0.84 2.32 2.32169 0.85 2.33 2.33170 0.85 2.34 2.34171 0.86 2.35 2.35172 0.86 2.36 2.36173 0.87 2.38 2.38174 0.87 2.39 2.39

175 0.88 2.4 2.4176 0.88 2.41 2.41177 0.89 2.42 2.42178 0.89 2.44 2.44179 0.9 2.45 2.45180 0.9 2.46 2.46181 0.91 2.47 2.47182 0.91 2.48 2.48183 0.92 2.5 2.5184 0.92 2.51 2.51185 0.93 2.52 2.52186 0.93 2.53 2.53

187 0.94 2.55 2.55188 0.94 2.56 2.56189 0.95 2.57 2.57190 0.95 2.59 2.59191 0.96 2.6 2.6192 0.96 2.61 2.61193 0.97 2.62 2.62194 0.97 2.64 2.64195 0.98 2.65 2.65

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196 0.98 2.66 2.66197 0.99 2.68 2.68198 0.99 2.69 2.69199 1 2.7 2.7200 1 2.72 2.72201 1.01 2.73 2.73

202 1.01 2.75 2.75203 1.02 2.76 2.76204 1.02 2.77 2.77205 1.03 2.79 2.79206 1.03 2.8 2.8207 1.04 2.82 2.82208 1.04 2.83 2.83209 1.05 2.84 2.84210 1.05 2.86 2.86211 1.06 2.87 2.87212 1.06 2.89 2.89213 1.07 2.9 2.9

214 1.07 2.92 2.92215 1.08 2.93 2.93216 1.08 2.94 2.94217 1.09 2.96 2.96218 1.09 2.97 2.97219 1.1 2.99 2.99220 1.1 3 3221 1.11 3.02 3.02222 1.11 3.03 3.03223 1.12 3.05 3.05224 1.12 3.06 3.06225 1.13 3.08 3.08

226 1.13 3.1 3.1227 1.14 3.11 3.11228 1.14 3.13 3.13229 1.15 3.14 3.14230 1.15 3.16 3.16231 1.16 3.17 3.17232 1.16 3.19 3.19233 1.17 3.21 3.21234 1.17 3.22 3.22235 1.18 3.24 3.24236 1.18 3.25 3.25237 1.19 3.27 3.27

238 1.19 3.29 3.29239 1.2 3.3 3.3240 1.2 3.32 3.32241 1.21 3.34 3.34242 1.21 3.35 3.35243 1.22 3.37 3.37244 1.22 3.39 3.39245 1.23 3.4 3.4246 1.23 3.42 3.42

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247 1.24 3.44 3.44248 1.24 3.46 3.46249 1.25 3.47 3.47250 1.25 3.49 3.49251 1.26 3.51 3.51252 1.26 3.53 3.53

253 1.27 3.54 3.54254 1.27 3.56 3.56255 1.28 3.58 3.58256 1.28 3.6 3.6257 1.29 3.61 3.61258 1.29 3.63 3.63259 1.3 3.65 3.65260 1.3 3.67 3.67261 1.31 3.69 3.69262 1.31 3.71 3.71263 1.32 3.72 3.72264 1.32 3.74 3.74

265 1.33 3.76 3.76266 1.33 3.78 3.78267 1.34 3.8 3.8268 1.34 3.82 3.82269 1.35 3.84 3.84270 1.35 3.86 3.86271 1.36 3.88 3.88272 1.36 3.9 3.9273 1.37 3.92 3.92274 1.37 3.94 3.94275 1.38 3.96 3.96276 1.38 3.97 3.97

277 1.39 3.99 3.99278 1.39 4.01 4.01279 1.4 4.03 4.03280 1.4 4.06 4.06281 1.41 4.08 4.08282 1.41 4.1 4.1283 1.42 4.12 4.12284 1.42 4.14 4.14285 1.43 4.16 4.16286 1.43 4.18 4.18287 1.44 4.2 4.2288 1.44 4.22 4.22

289 1.45 4.24 4.24290 1.45 4.26 4.26291 1.45 4.28 4.28292 1.46 4.31 4.31293 1.46 4.33 4.33294 1.47 4.35 4.35295 1.47 4.37 4.37296 1.48 4.39 4.39297 1.48 4.41 4.41

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298 1.49 4.44 4.44299 1.49 4.46 4.46300 1.5 4.48 4.48301 1.5 4.5 4.5302 1.51 4.53 4.53303 1.51 4.55 4.55

304 1.52 4.57 4.57305 1.52 4.6 4.6306 1.53 4.62 4.62307 1.53 4.64 4.64308 1.54 4.66 4.66309 1.54 4.69 4.69310 1.55 4.71 4.71311 1.55 4.74 4.74312 1.56 4.76 4.76313 1.56 4.78 4.78314 1.57 4.81 4.81315 1.57 4.83 4.83

316 1.58 4.85 4.85317 1.58 4.88 4.88318 1.59 4.9 4.9319 1.59 4.93 4.93320 1.6 4.95 4.95321 1.6 4.98 4.98322 1.61 5 5323 1.61 5.03 5.03324 1.62 5.05 5.05325 1.62 5.08 5.08326 1.63 5.1 5.1327 1.63 5.13 5.13

328 1.64 5.16 5.16329 1.64 5.18 5.18330 1.65 5.21 5.21331 1.65 5.23 5.23332 1.66 5.26 5.26333 1.66 5.29 5.29334 1.67 5.31 5.31335 1.67 5.34 5.34336 1.68 5.37 5.37337 1.68 5.39 5.39338 1.69 5.42 5.42339 1.69 5.45 5.45

340 1.7 5.47 5.47341 1.7 5.5 5.5342 1.71 5.53 5.53343 1.71 5.56 5.56344 1.72 5.58 5.58345 1.72 5.61 5.61346 1.73 5.64 5.64347 1.73 5.67 5.67348 1.74 5.7 5.7

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349 1.74 5.73 5.73350 1.75 5.75 5.75351 1.75 5.78 5.78352 1.76 5.81 5.81353 1.76 5.84 5.84354 1.77 5.87 5.87

355 1.77 5.9 5.9356 1.78 5.93 5.93357 1.78 5.96 5.96358 1.79 5.99 5.99359 1.79 6.02 6.02360 1.8 6.05 6.05361 1.8 6.08 6.08362 1.81 6.11 6.11363 1.81 6.14 6.14364 1.82 6.17 6.17365 1.82 6.2 6.2366 1.83 6.23 6.23

367 1.83 6.27 6.27368 1.84 6.3 6.3369 1.84 6.33 6.33370 1.85 6.36 6.36371 1.85 6.39 6.39372 1.86 6.42 6.42373 1.86 6.46 6.46374 1.87 6.49 6.49375 1.87 6.52 6.52376 1.88 6.55 6.55377 1.88 6.59 6.59378 1.89 6.62 6.62

379 1.89 6.65 6.65380 1.9 6.69 6.69381 1.9 6.72 6.72382 1.91 6.75 6.75383 1.91 6.79 6.79384 1.92 6.82 6.82385 1.92 6.86 6.86386 1.93 6.89 6.89387 1.93 6.92 6.92388 1.94 6.96 6.96389 1.94 6.99 6.99390 1.95 7.03 7.03

391 1.95 7.06 7.06392 1.96 7.1 7.1393 1.96 7.13 7.13394 1.97 7.17 7.17395 1.97 7.21 7.21396 1.98 7.24 7.24397 1.98 7.28 7.28398 1.99 7.32 7.32399 1.99 7.35 7.35

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400 2 7.39 7.39401 2 7.43 7.43402 2.01 7.46 7.46403 2.01 7.5 7.5404 2.02 7.54 7.54405 2.02 7.58 7.58

406 2.03 7.61 7.61407 2.03 7.65 7.65408 2.04 7.69 7.69409 2.04 7.73 7.73410 2.05 7.77 7.77411 2.05 7.81 7.81412 2.06 7.85 7.85413 2.06 7.89 7.89414 2.07 7.92 7.92415 2.07 7.96 7.96416 2.08 8 8417 2.08 8.04 8.04

418 2.09 8.08 8.08419 2.09 8.13 8.13420 2.1 8.17 8.17421 2.1 8.21 8.21422 2.11 8.25 8.25423 2.11 8.29 8.29424 2.12 8.33 8.33425 2.12 8.37 8.37426 2.13 8.41 8.41427 2.13 8.46 8.46428 2.14 8.5 8.5429 2.14 8.54 8.54

430 2.15 8.58 8.58431 2.15 8.63 8.63432 2.16 8.67 8.67433 2.16 8.71 8.71434 2.17 8.76 8.76435 2.17 8.8 8.8436 2.18 8.85 8.85437 2.18 8.89 8.89438 2.19 8.94 8.94439 2.19 8.98 8.98440 2.2 9.03 9.03441 2.2 9.07 9.07

442 2.21 9.12 9.12443 2.21 9.16 9.16444 2.22 9.21 9.21445 2.22 9.25 9.25446 2.23 9.3 9.3447 2.23 9.35 9.35448 2.24 9.39 9.39449 2.24 9.44 9.44450 2.25 9.49 9.49

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451 2.25 9.54 9.54452 2.26 9.58 9.58453 2.26 9.63 9.63454 2.27 9.68 9.68455 2.27 9.73 9.73456 2.28 9.78 9.78

457 2.28 9.83 9.83458 2.29 9.87 9.87459 2.29 9.92 9.92460 2.3 9.97 9.97461 2.3 10.02 10.02462 2.31 10.07 10.07463 2.31 10.12 10.12464 2.32 10.18 10.18465 2.32 10.23 10.23466 2.33 10.28 10.28467 2.33 10.33 10.33468 2.34 10.38 10.38

469 2.34 10.43 10.43470 2.35 10.49 10.49471 2.35 10.54 10.54472 2.36 10.59 10.59473 2.36 10.64 10.64474 2.37 10.7 10.7475 2.37 10.75 10.75476 2.38 10.8 10.8477 2.38 10.86 10.86478 2.39 10.91 10.91479 2.39 10.97 10.97480 2.4 11.02 11.02

481 2.4 11.08 11.08482 2.41 11.13 11.13483 2.41 11.19 11.19484 2.42 11.25 11.25485 2.42 11.3 11.3486 2.43 11.36 11.36487 2.43 11.42 11.42488 2.44 11.47 11.47489 2.44 11.53 11.53490 2.45 11.59 11.59491 2.45 11.65 11.65492 2.46 11.7 11.7

493 2.46 11.76 11.76494 2.47 11.82 11.82495 2.47 11.88 11.88496 2.48 11.94 11.94497 2.48 12 12498 2.49 12.06 12.06499 2.49 12.12 12.12500 2.5 12.18 12.18

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First Order Differential Equation

y' = f(t, y)--------------------------------------------Fourth Order Runge-Kutta

K 1 = f(t n , y n)

K 2 = f(t n+h/2, y n+K 1h/2)

K 3 = f(t n+h/2, y n+K 2h/2)

K 4 = f(t n+h, y n+K 3h)

yn+1 = y n + h (K 1 + 2K 2 + 2K 3 + K 4)/6