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Question
Mathematics
The solution of the differential equation x(dy/dx)+2y=x2 is:
Q. The solution of the differential equation
x
d
x
d
y
+
2
y
=
x
2
is:
1271
223
KEAM
KEAM 2006
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A
y
=
4
x
2
x
2
+
c
B
y
=
4
x
2
+
c
C
y
=
x
2
x
4
+
c
D
y
=
4
x
2
x
4
+
c
E
y
=
4
x
3
+
x
2
c
Solution:
x
=
d
x
d
y
+
2
y
=
x
2
On differentiating w.r.t
x
,
we get
d
x
d
y
+
x
2
y
=
x
Integrating factor
=
e
∫
x
2
d
x
=
x
2
∴
Required solution is
y
.
x
2
=
∫
x
3
d
x
=
4
x
4
+
c
=
4
x
4
+
c
∴
y
=
4
x
2
x
4
+
c