Find the equation of a curve passing through the point (0, 2) given that the sum of
the coordinates of any point on the curve exceeds the magnitude of the slope of
the tangent to the curve at that point by 5 18 The Integrating Factor of the differential equation 
22
xdy
y
x
dx −
=
 is
(A) e–x
(B) e–y
(C) 1
x
(D) x
19 The Integrating Factor of the differential equation
2
(1
y) dx
yx
dy
−
+
 = 
( 1
1)
 
 
ay
y
 is
(A)
12
y  1
(B)
2
1
y −1
(C)
112
−y
(D)
2
1
1
y
−
Miscellaneous Examples
Example 24 Verify that the function y = c1 eax cos bx + c2 eax sin bx, where c1, c2 are
arbitrary constants is a solution of the differential equation
(
)
2
2
2
2
2
0
d y
ady
a
b
y
dx
dx
−
+
+
=
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DIFFERENTIAL EQUATIONS
415
Solution The given function is
y = eax [c1 cosbx + c2 sinbx]