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JEE Main Math Class 12 Differential Equations Part 2 Questions
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© examsnet.com
Question : 62
Total: 124
Let
y
=
y
(
x
)
be the solution of the differential equation
d
y
d
x
=
4
y
3
+
2
y
x
2
3
x
y
2
+
x
3
,
y
(
1
)
=
1
.
If for some
n
∈
ℕ
,
y
(
2
)
∈
[
n
−
1
,
n
)
, then
n
is equal to __
[25-Jul-2022-Shift-2]
Your Answer:
Validate
Solution:
d
y
d
x
=
y
x
(
4
y
2
+
2
x
2
)
(
3
y
2
+
x
2
)
Put
y
=
v
x
⇒
d
y
d
x
=
v
+
x
d
v
d
x
⇒
v
+
x
d
v
d
x
=
v
(
4
v
2
+
2
)
(
3
v
2
+
1
)
⇒
x
d
v
d
x
=
v
(
(
4
v
2
+
2
−
3
v
2
−
1
)
3
v
2
+
1
)
⇒
∫
(
3
v
2
+
1
)
d
v
v
3
+
v
=
∫
d
x
x
⇒
ln
|
v
3
+
v
|
=
ln
x
+
c
⇒
ln
|
(
y
x
)
3
+
(
y
x
)
|
=
ln
x
+
C
↓
y
(
1
)
=
1
⇒
C
=
ln
2
∴
for
y
(
2
)
ln
(
y
3
8
+
y
2
)
=
2
ln
2
⇒
y
3
8
+
y
2
=
4
⇒
[
y
(
2
)
]
=
2
⇒
n
=
3
© examsnet.com
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