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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
Find the sing...
Question
Find the singular solution of the differential equation
y
=
p
x
+
p
−
p
2
. Where
p
=
d
y
d
x
.
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Solution
Given the differential equation,
y
=
p
x
+
p
−
p
2
.......(1)
Now, differentiating both sides with respect to
x
we get,
p
=
p
+
(
x
+
1
−
2
p
)
d
p
d
x
[ Since
d
y
d
x
=
p
]
or,
(
x
+
1
−
2
p
)
d
p
d
x
=
0
or,
x
+
1
=
2
p
and
d
p
d
x
=
0
.
or,
p
=
x
+
1
2
gives particular solution and
d
p
d
x
=
0
leads to general solution.
Now putting
p
=
x
+
1
2
in (1) we get,
y
=
(
x
+
1
)
2
2
−
(
x
+
1
)
2
4
or,
y
=
(
x
+
1
)
2
4
or,
(
x
+
1
)
2
=
4
y
.
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Q.
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