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KEAM 2012 Math Paper
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© examsnet.com
Question : 18
Total: 120
An integrating factor of the differential equation
x
dy
−
y
dx
+
x
2
e
x
dx
=
0
is
1
x
log
√
1
+
x
2
√
1
+
x
2
x
1
1
+
x
2
Validate
Solution:
Given differential equation is
x
d
y
−
y
d
x
+
x
2
e
x
d
x
=
0
⇒
x
d
y
+
d
x
(
x
2
e
x
−
y
)
=
0
⇒
d
y
d
x
−
y
x
=
−
x
e
x
∴
I
F
=
e
∫
P
d
x
=
e
∫
−
1
x
d
x
=
e
−
log
x
=
1
x
© examsnet.com
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