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Byju's Answer
Standard XII
Mathematics
Integration as Antiderivative
Find the solu...
Question
Find the solution of
d
y
d
x
=
e
x
−
y
+
x
2
e
−
y
.
A
e
y
=
e
x
−
x
3
3
+
c
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B
e
y
=
e
x
+
x
3
4
+
c
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C
e
y
=
e
x
−
x
3
4
+
c
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D
e
y
=
e
x
+
x
3
3
+
c
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Solution
The correct option is
C
e
y
=
e
x
+
x
3
3
+
c
Given
d
y
d
x
=
e
x
−
y
+
x
2
e
−
y
⇒
d
y
d
x
=
e
x
e
y
+
x
2
e
y
⇒
e
y
d
y
=
(
e
x
+
x
2
)
d
x
.
Now integrating both sides.
e
y
=
e
x
+
x
3
3
+
c
.
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Q.
The solution of the equation
d
y
d
x
−
e
x
−
y
+
x
2
e
−
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is
[MP PET 2004]