The solution of $\left(2 x-10 y^3\right) \frac{dy}{d x}+y=0$ is :
Answer & explanation
Correct answer: option 3
$y \frac{d x}{d y} \Rightarrow-2 x+10 y^3 \Rightarrow \frac{d x}{d y}+\frac{2 x}{y}=10 y^2$
$\Rightarrow P=\frac{2}{y}, Q=10 y^2$
∴ I.F. $=e^{\int \frac{2}{y} d y}=e^{2 \log y}=e^{\log y^2}=y^2$
∴ Solution is $x . y^2=\int y^2 . 10 y^2 d y+c$
$\Rightarrow x . y^2=\frac{10 . y^5}{5}+c$
Hence (3) is the correct answer.