Question 1. [3 marks] Find the general solution of
xy 4y = 5x3
Solution a. Divide the given equation by x,
4
y y = 5x2
x
For this nonhomogeneous linear ODE, we have
4
p= ,
x
r = 5x2 ,
h=
p dx = 4 ln x
The general solution is
y (x) = eh
eh r dx + c
5
= x4
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FEBRUARY 2010 MIDTERM TEST 1
MAT234H2
Dierential Equations
Instructors: M. Chugunova, G. Simpson
NO AIDS ALLOWED
Duration: 100 minutes
Total Marks: 80
Marker:
Instructions: All answers go on the exam sh
MARCH 2010 MIDTERM TEST II
MAT234H1S Dierential Equations
Instructors: M. Chugunova, G. Simpson
Duration: 100 minutes
All answers go in the exam booklet.
Total Marks: 80
Question 1. (20 marks )
y + 4 y = 3 cos(2 t) + t
[a] Find the general solution of the