Find the general solution of the differential equation

Before starting solving the differential equation, we should know the type of differential equation.

This is the linear type differential equation,

y dx – (x + 2y²)dy = 0

It is of the form + Rx = S where R and S are either constants or function of y.

To solve these type of equations, we need first to find the integrating factor which is = and multiply both sides of the general form of the equation and after that integrate the whole equation.

First, convert the given equation in general form equation,

R = and S = 2y

Now find the I.F. =

Multiplying both sides by I.F. we get,

Integrating both sides with respect to y, we get,