Let f:\mathbb{R}\to\mathbb{R} be a differentiable function with f(0)=0.If y=f(x) satisfies the differential equation \frac{dy}{dx}=(2+5y)(5y-2), then the value of \text{lim}_{x\to\infty}f(x) is _____. [JEE Adv 2018 P2]

Differential Equations

Section: Mathematics

Question : 9 of 23

Marks: +1, -0

Let f:ℝ→ℝ be a differentiable function with f(0)=0.If y=f(x) satisfies the differential equation

=(2+5y)(5y−2), then the value of

lim

x→∞

f(x) is _____.

[JEE Adv 2018 P2]

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