Differential Equations

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

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

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

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