$x=y^2 \sin y+y \cos ^2 y$

$x=y^2 \sin y+2 y \cos ^2 \frac{y}{2}$

$x=y^2 \sin y+y \cos ^2 \frac{y}{2}$

$x=y^2 \sin y-y \cos ^2 y$

$y \log (x+y)=c x$

$\log (x+y)=c y$

$x \log (x+y)=c y$

$\log (x+y)=c x$

$x+\cot \left(\frac{x-y+1}{2}\right)=C$

$x+\cot (x-y+1)=C$

$x-\cot \left(\frac{x-y+1}{2}\right)=C$

$x-\cot (x-y+1)=C$

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

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

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

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