 
Summary: Math 2090 Spring 2005
Sections 4 and 7 P. Achar
Hour Exam 1 Solutions
February 15, 2005
1. (3 points each) Give examples (not taken from later in the exam) of the following types of differential
equations: There are many possible answers to this question, of course. Here are some possibilities:
(a) Separable:
Solution: 5y y2
= sin x
(b) Firstorder linear homogeneous:
Solution: y + x5
y = 0
(c) Thirdorder linear nonhomogeneous:
Solution: y + 5y  ex
y + 2y = cos x
(d) Secondorder nonlinear:
Solution: y + y2
= tan x
2. (4 points) What is the complementary function for a nonhomogeneous linear equation?
Solution: the general solution to the associated homogeneous equation
