Sheet (1)
(Ordinary Differential Equations)
1. Determine the order of the following differential equations and
the degree:
a. y` + xy = x2
b. (y``)3 + y` = x3
c. [ 1 + (y`)2 ] 3/2 = 4 y```
d. (
)
e.
2. Determine which of the following differential equations are
Linear or non-Linear and study the Homogenous:
a. x3 y``` - 4 x2 y`` + xy` + y = o
b. x3 y`` + 2y` + y2 = 0
c. x10 y`` + (x2 + 1) y = 0
d. x3 y4 + ( 1 + x) y``` + sinx y + cosx = 0
e. x y``` y + y`` + ex y` + y = o
3. Find the particular solution of the differential equation: y`` = ex
where, y`(1) = 0 & y(1) = 1
4. Show that the function y = A e3x + B e-3x is a solution to the
differential equation: y``- 9y = 0, where A, B are arbitrary
constants.
5. Show that the function y = A cosax + B sinax is a solution to the
differential equation: y``+ a2y = 0, where A, B are arbitrary
constants.