The general solution of the differential equation $ydx - (x + 2y^2) dy = 0$ is :

$x = 2y^2 + Cy$, C is a constant

$ydx - (x + 2y^2)dy = 0$

⇒ $y dx = (x + 2y^2)dy$

so $y dx - x dy = 2y^2 dy$

⇒ $\frac{ydx - xdy}{y^2}=2dy$

integrating both sides

$\int \frac{ydx - xdy}{y^2} = \int 2 dy$

we know that

$\int d(\frac{x}{y})$

= $\int \frac{y dx - xdy}{y^2}$

⇒ $\int d(\frac{x}{y}) = \int 2 dy$

⇒ $\frac{x}{y} = 2y + C$

⇒ $x = 2y^2 + Cy$