$(\sin 2 x) y=\sin ^2 x+C$

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

$\left(1+\sin ^2 x\right) y=\sin x+\frac{\sin ^3 x}{3}+C$

$(\sin 2 x) y=\sin x+\sin ^2 x+C$

$y=c e^x+1+x$

$y=c e^x-x$

$y=c e^{-x}-1-x$

$y=c e^x-1-x$

$\log \left|x^2 y\right|=\frac{2}{x}+\frac{1}{y}+x-1$

$\log \left|\frac{1}{4} x^2 y\right|=\frac{1}{x}+\frac{2}{y}+x-1$

$\log \left|\frac{1}{2} x^2 y\right|=\frac{1}{x}+\frac{1}{y}-x-\frac{1}{2}$

$\log \left|\frac{1}{3} x^2 y\right|=\frac{1}{x}+\frac{1}{y}-x+\frac{1}{2}$

$x^2-x y-y^2+3 x+3 y+c=0$

$x^2-x y-y^2-3 x-3 y+c=0$

$x^2+x y-y^2-3 x-3 y+c=0$

$x^2+x y+y^2+3 x-3 y+c=0$