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Byju's Answer
Standard XII
Mathematics
Particular Solution of a Differential Equation
The solution ...
Question
The solution of
y
d
x
−
x
d
y
+
3
x
2
y
2
e
x
3
d
x
=
0
A
x
y
+
e
x
3
=
c
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B
x
y
−
e
x
3
=
c
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C
x
y
=
−
e
x
3
+
c
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D
none of these
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Solution
The correct option is
A
x
y
+
e
x
3
=
c
∫
y
d
x
−
x
d
y
y
2
+
3
∫
x
2
e
x
3
d
x
=
0
Consider
∫
y
d
x
−
x
d
y
y
2
We know that
d
d
x
(
x
y
)
=
y
d
x
−
x
d
y
y
2
∫
d
d
x
(
x
y
)
d
x
=
x
y
+
c
1
Consider
3
∫
x
2
e
x
3
d
x
=
∫
3
x
2
e
x
3
d
x
Let
t
=
x
3
⇒
d
t
=
3
x
2
d
x
=
∫
e
t
d
t
=
e
t
+
c
2
=
e
x
3
+
c
2
∴
∫
y
d
x
−
x
d
y
y
2
+
3
∫
x
2
e
x
3
d
x
=
0
x
y
+
c
1
+
e
x
3
+
c
2
=
0
⇒
x
y
+
e
x
3
=
−
(
c
1
+
c
2
)
⇒
x
y
+
e
x
3
=
c
where
c
=
−
(
c
1
+
c
2
)
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0
Similar questions
Q.
Find the differentiation of a function represented by
y
=
e
x
3
with respect to
x
.
Q.
Assertion :Area bounded by the curve
y
=
e
x
3
between the ordinates x=a and x=b is
∫
b
a
e
x
3
d
x
Reason:
y
=
e
x
3
is always an increasing function
Q.
Assertion(A):Area enclosed by the curve
y
=
e
x
3
between the lines
x
=
a
,
x
=
b
and
x
-axis is
∫
b
a
e
x
3
d
x
Reason(R):
e
x
3
is an increasing functions.
Q.
Solve for x :
e
x
3
=
e
x
3
×
x
2
Q.
Assertion :Area enclosed by the curve
y
=
e
x
2
between the lines
x
=
a
,
x
=
b
and
x
−
axis is
∫
b
a
e
x
3
Reason:
e
x
3
is an increasing function.
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