jee-advanced 2018 Q10

jee-advanced · India · paper2 3 marks Differential equations Solving Separable DEs with Initial Conditions
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 the value of $\lim _ { x \rightarrow - \infty } f ( x )$ is $\_\_\_\_$ .
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 the value of $\lim _ { x \rightarrow - \infty } f ( x )$ is $\_\_\_\_$ .