Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function with $f(0)=0$. If $y=f(x)$ satisfies the differential equation \[ \frac{d y}{d x}=(2+5 y)(5 y-2) \] then what is the value of $\lim _{x \rightarrow-\infty} f(x)$?
JEE · Math · previous-year question
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