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Byju's Answer
Standard XII
Mathematics
Degree of a Differential Equations
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Question
Find the general solution of the differential equation
y
=
p
x
+
p
2
where
p
=
d
y
d
x
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Solution
Given the differential equation is
y
=
p
x
+
p
2
.
Now differentiating both sides with respect to
x
we get,
p
=
p
+
{
x
+
2
p
}
d
p
d
x
[ Since
p
=
d
y
d
x
]
or,
d
p
d
x
=
0
and
x
+
2
p
=
0
or,
p
=
c
......(1)[ Where
c
is integrating constant] and
x
+
2
p
=
0
......(2).
Equation (1) will lead us to a general solution and equation (2) will lead us singular solution.
So the general solution is
y
=
c
x
+
c
2
. [ putting
p
=
c
in the given differential equation]
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