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Mathematics
Mathematics
Problem
Let
y
=
(
k
x
+
3
)
e
x
2
y=(k x + 3)\, e^{x^{2}}
y
=
(
k
x
+
3
)
e
x
2
, where
k
k
k
is a real constant. For which value of
k
k
k
does
y
y
y
satisfy the differential equation
d
y
d
x
=
(
6
x
2
+
6
x
+
3
)
e
x
2
\dfrac{dy}{dx} = (6x^{2}+6x+3)\, e^{x^{2}}
d
x
d
y
=
(
6
x
2
+
6
x
+
3
)
e
x
2
? Provide the value of
k
k
k
.
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