8/13/2019 Paper Applied Differential Equations
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Applied differential EquationsMidterm examinations
Center for High Energy Physics
BS (4 Years) Morning program Semester 3rd
Q.1 Define the following (2+2+2) Trajectory of the family of
curves Linear differential equation Boundary value problem
Q.2Find the general solution of the following differential
equations. (5+5)
= sin(x+y)+cos(x+y)
xdy+ydx+3x3y4dy=0Q.3Let F be the constant forcegenerated by the
motor of an automobile of mass M, ant its
velocity v be given by
M
= F-kv
Where k is a constant. Express v in term of given that v=0 when
t=0 (4)
Q.4Find the particular solution of the following differential
equation (5)
=
, x(0)=-1
Q.5The slope at any point (x,y) of the curve is 3x-2y. if the
curve passes through the
origin, determine the equation of the curve. (5)
Q.6Define Exact Differential Equation (2+6)
Prove that a necessary and sufficient condition for the
differential equation
M(x,y)dx+N(x,y)dy=0 to be exact is
=
.
Q.7Find the orthogonal trajectory of the following family of
curves. (5)
Q.8Define Newtons Law of Cooling. (2+5)
A Metal bar at a temperature of 100F is placed in a room at a
constant temperature of
0F. If after 20 minutes the temperature of the bar is 50F, find
a) the time it will takethe bar to reach the temperature of 25F and
b) the temperature of the bar after 10
minutes.
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