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TN XII Math
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Q)
On putting
y
=
v
x
,
the homogeneous differential equation
x
2
d
y
+
y
(
x
+
y
)
d
x
=
0
becomes
(
1
)
x
d
v
+
(
2
v
+
v
2
)
d
x
=
0
(
2
)
v
d
x
+
(
2
x
+
x
2
)
d
v
=
0
(
3
)
v
2
d
x
−
(
x
+
x
2
)
d
v
=
0
(
4
)
v
d
v
+
(
2
x
+
x
2
)
d
x
=
0
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