The solution of $\left(2 x-10 y^3\right) \frac{dy}{d x}+y=0$ is :

$x y^2=2 y^5+c$

$y \frac{d x}{d y} \Rightarrow-2 x+10 y^3 \Rightarrow \frac{d x}{d y}+\frac{2 x}{y}=10 y^2$

$\Rightarrow P=\frac{2}{y}, Q=10 y^2$

∴  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.