Download Solve the following differential equations a) b) c) d) Question 2: a) If

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University of Bahrain
College of Science
Department of Mathematics
Second Semester 2002/2003
MATH 205
Test 1
Question 1:
Solve the following differential equations
a)
(e y + y cos x)dx + (sin x − sin y + xe y )dy = 0
b)
(x 2 − y 2 )dx + 2 xy dy = 0
c)
y ′ = csc x − y cot x.
d)
dy
( xy + y 2 ) + ( x 2 + xy )
=0
dx
Question 2:
a)
b)
If a differential equation is seperable, Show that it is exact. Is the
converse true.
Find the orthogonal Trajectories of
x + ( y − c) 2 = c 2 .
1
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