February 2, 2005
MA205 Test I
Page 1 of 1
[12 marks ] 1. Identify (Dont solve), the equation as seperable, linear, exact, or having an integrating factor
that is function of either x alone or y alone. Justify your answers.
(x2 sin x + 4y )dx + xdy = 0
[10
MA205 Test 1-Version2, Oct. 26th, 2005
[10 marks ] [1] Show that xy 2 is an integrating factor for (2y 6x)dx + (3x
4x2
)dy = 0. Do
y
not solve.
[15 marks ] [2] Consider the Bernoulli type equation
dy
5
5y = xy 3 .
dx
2
(a) Use the substitution v = y 2 a
WILFRID LAURIER UNIVERSITY
WATERLOO, ONTARIO
Fall Term, 2006
Course ID: MA205
Name:
Student ID:
Course Title: Dierential Equations I
Instructor: C. Stoica
Number of Pages: 9 plus cover page
Length of Examination: 2 hours
Examination Aids Allowed: Non-prog
Page 1 of 7
M A205 Midterm Test
1-
1. Solve the initial value problem
du
-=(1+y2)tanx,
dx
4wcKs
y (O)=&.
dy
5
[6marks] 2. Consider the Bernoulli t ypc c quation - - 5y = -xu3.
dx
(:a) Use the substitution
2
dv
v = Y -2 a nd show that the equation in varia
WILFRID LAURIER UNIVERSITY
WATERLOO, ONTARIO
Fall Term, 2005
Course ID: MA205
Name:
Student ID:
Course Title: Dierential Equations I
Professor: Dr. C. Stoica
Number of Pages: 8 plus cover page
Length of Examination: 2 hours
Examination Aids Allowed: Non-p