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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a differentiable function with
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
. If
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
satisfies the differential equation
d
y
d
x
=
(
2
+
5
y
)
(
5
y
−
2
)
\frac{dy}{dx} = (2+5y)(5y-2)
d
x
d
y
=
(
2
+
5
y
)
(
5
y
−
2
)
, then the value of
lim
x
→
−
∞
f
(
x
)
\lim_{x \to -\infty} f(x)
lim
x
→
−
∞
f
(
x
)
is \_\_\_\_\_\_. [JEE(Advanced) 2018]
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