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Byju's Answer
Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
Solution of t...
Question
Solution of the differential equation
y
e
x
/
y
d
x
=
(
x
e
x
/
y
+
y
2
sin
y
)
d
y
, is
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Solution
Given,
y
e
x
y
d
x
=
(
x
e
x
y
+
y
2
sin
y
)
d
y
e
x
y
d
x
=
(
x
y
e
x
y
+
y
sin
y
)
d
y
d
x
d
y
=
x
y
+
y
sin
y
e
x
y
substitute
v
=
x
y
→
d
x
d
y
=
y
d
v
d
y
+
v
y
d
v
d
y
+
v
=
v
+
y
sin
y
e
v
y
d
v
d
y
=
y
sin
y
e
v
e
v
d
v
=
sin
y
d
y
integrating on both sides,
e
v
=
−
cos
y
+
c
∴
e
x
y
+
cos
y
=
c
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0
Similar questions
Q.
The solution of the differential equation.
y
e
x
/
y
d
x
=
(
x
e
x
/
y
+
y
2
sin
y
)
d
y
is.
Q.
y
e
x
/
y
d
x
=
(
x
e
x
/
y
+
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d
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Q.
Solve the differential equation
y
e
x
y
d
x
=
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x
e
x
y
+
y
2
)
d
y
(
y
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)
Q.
Solve the differential equation
y
e
x
y
d
x
=
⎛
⎜
⎝
x
e
x
y
+
y
2
⎞
⎟
⎠
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y
≠
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)
.
Q.
The general solution of the differential equation
(
1
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x
y
)
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