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Question
Mathematics
If y(x)=xx, x>0, then y prime prime(2)-2 y prime(2) is equal to :
Q. If
y
(
x
)
=
x
x
,
x
>
0
, then
y
′′
(
2
)
−
2
y
′
(
2
)
is equal to :
424
127
JEE Main
JEE Main 2023
Differential Equations
Report Error
A
4
(
lo
g
e
2
)
2
−
2
B
8
lo
g
e
2
−
2
C
4
(
lo
g
e
2
)
2
+
2
D
4
lo
g
e
2
+
2
Solution:
y
′
=
x
x
y
′
=
x
x
(
1
+
ℓ
n
x
)
y
′′
=
x
x
(
1
+
ℓ
n
x
)
2
+
x
x
⋅
x
1
y
′′
(
2
)
=
4
(
1
+
ℓ
n
2
)
2
+
2
y
′
(
2
)
=
4
(
1
+
ℓ
n
2
)
y
′′
(
2
)
−
2
y
′
(
2
)
=
4
(
1
+
ℓ
n
2
)
2
+
2
−
8
(
1
+
ℓ
n
2
)
=
4
(
1
+
ℓ
n
2
)
[
1
+
ℓ
n
2
−
2
]
+
2
=
4
(
ℓ
n
2
)
2
−
1
)
+
2
=
4
(
ℓ
n
2
)
2
−
2