Solution of the differential equation $(x+2y^3)\frac{dy}{dx}=y$ is:

$x=y^2(c+y^2)$ $x=y(c-y^2)$ $x=2y(c-y^2)$ $x=y(c+y^2)$

$x=y(c+y^2)$

$(x+2y^3)\frac{dy}{dx}=y⇒\frac{dx}{dy}=\frac{x}{y}+2y^2$ [Bernoull’s Differential equation] $⇒\frac{dx}{dy}-\frac{x}{y}=2y^2$ where $I.F.=e^{\int-\frac{1}{y}dy}=\frac{1}{y};x.\frac{1}{y}=\int\frac{2y^2}{y}dy+c⇒\frac{x}{y}=y^2+c$