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JEE Main Math Class 12 Differential Equations Part 2 Questions
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© examsnet.com
Question : 36
Total: 124
If the solution curve
f
(
x
,
y
)
=
0
of the differential equation
(
1
+
log
e
x
)
d
x
d
y
−
x
log
e
x
=
e
y
,
x
>
0
, passes through the points
(
1
,
0
)
and
(
α
,
2
)
, then
α
α
is equal to :
[6-Apr-2023 shift 2]
e
√
2
c
2
e
c
2
e
2
e
√
2
e
2
c
2
Validate
Solution:
(
1
+
ℓ
ln
x
)
d
x
d
y
−
x
ℓ
ln
x
=
e
y
Let
x
ℓ
n
x
=
t
(
1
+
ln
x
)
d
x
d
y
=
d
t
d
y
d
t
d
y
−
t
=
e
y
P
=
−
1
,
Q
=
e
y
I
⋅
F
=
e
∫
−
d
y
=
e
−
y
Solution -
(
t
)
(
e
−
y
)
=
∫
(
e
−
y
)
(
e
y
)
d
y
t
(
e
−
y
)
=
y
+
c
(
x
ℓ
ln
x
)
e
−
y
=
y
+
c
pass
(
1
,
0
)
⇒
c
=
0
pass
(
α
,
2
)
α
α
=
e
2
e
2
Ans. Option 4
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