Differential Equations

$\left(y^2-2 x^2 y\right) d x=\left(x^2-2 x y^2\right) d y$

$x^2 d y-y d x=\sqrt{x^2+y^2} d x$

$\frac{d y}{d x}=\frac{y^2}{x+\sqrt{x y}}$

$\left(1+2 e^{\frac{x}{y}}\right)+2 e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) \frac{d y}{d x}=0$