Math 267 Exam Review IINo SI tomorrow

Sessions resume W @ 5:10 Carver 0148

Section 4.1

Find the largest interval where

(t2 - 1)y'' + 3ty' + cos t y = et y(0) = 4, y'(0) = 5

is guaranteed to have a unique solution.

Don’t forget about linear independence

Section 4.2 Reduction of orderFind the General solution to:

𝑦′′ −3

𝑥𝑦′ +

4

𝑥2𝑦 = 0 𝑦1 = 𝑥2

4.2 Answer

See example 2 from section 4.2

Section 4.3

Case 1.

Case 2.

Case 3.

Answers and more practice

http://tutorial.math.lamar.edu/Classes/DE/RealRoots.aspx

http://tutorial.math.lamar.edu/Classes/DE/ComplexRoots.aspx

http://tutorial.math.lamar.edu/Classes/DE/RepeatedRoots.aspx

A harder example

𝑦(4) − 2𝑦′′ + 𝑦 = 0

Section 4.4

Find the solution to the following DE𝑦′′ − 6𝑦′ + 9𝑦 = −12𝑒3𝑥 + 9𝑥

Problem is similar to example 9 from section 4.4

Section 4.6

Section 4.6 Solve the Following DE’s:

Answer + more practice

http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx

Section 4.7

Answers

http://tutorial.math.lamar.edu/Classes/DE/EulerEquations.aspx

Section 4.9

𝑥′ − 4𝑥 + 𝑦′′ = 𝑡2

𝑥′ + 𝑥 + 𝑦′ = 0

Section 3.1 and 3.2

A tank has pure water flowing into it at 10 l/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 l/min. Initially, the tank contains 10 kg of salt in 100 l of water. How much salt will there be in the tank after 30 minutes?

Answers

See Example 2 from section 4.9

3.1: http://www.math.washington.edu/~conroy/m125-general/mixingTankExamples/mixingTankExamples01.pdf

Section 4.9 Section 3.2

• Suppose a student carrying a flu virus returns to an isolated college campus of 2000 students. If it is assumed that the rate at which the virus spreads is proportional no only to the number of x infected students but also to the number of students not infected, determine the number of infected students after 7 days if it is further observed that after 4 days x(4) = 120

𝑥′ − 4𝑥 + 𝑦′′ = 𝑡2

𝑥′ + 𝑥 + 𝑦′ = 0

3.2 Answer

See example 1 from section 3.2

Section 5.1

A mass weighing 8 lbs stretches a spring 2 feet. Assuming that a damping force numerically equal to 2 times the instantaneous velocity acts on the system, determine the equation of motion if the mass is initially released from thee equilibrium position with an upward velocity of 3ft/s.

Answer

See example 4 from section 5.1