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

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

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

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

Order is 2 and degree is 3

Order is 3 and degree is 3

Order is 3 and degree is 2

Order is 2 and degree is not defined

$x+y+3 \log \left|\frac{x+1}{y+1}\right|=c$

$x+y+3 \log \left|\frac{y+1}{x+1}\right|=c$

$x-y+3 \log \left|\frac{x+1}{y+1}\right|=c$

$x-y+3 \log \left|\frac{y+1}{x+1}\right|=c$

$1+\left(\frac{d y}{d x}\right)^2=\frac{r^2}{(y-3)^2}$

$1+\left(\frac{d y}{d x}\right)^2=\frac{r^2}{y-3}$

$\left(\frac{d y}{d x}\right)^2=\frac{r^2}{(y-3)^2}$

$\left(\frac{d y}{d x}\right)^2=\frac{r^2}{y-3}$