$\log |x+2 y|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{y-x}{\sqrt{3} x}\right)=C$

$\log |2 x-y|+\frac{2}{3} \tan ^{-1}\left(\frac{x-y}{\sqrt{3} x}\right)=C$

$\log |x y-x|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 y+1}{\sqrt{3}}\right)=C$

$\log |x+y|+\frac{2}{3} \tan ^{-1}\left(\frac{x-2 y}{\sqrt{3 x}}\right)=C$

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

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

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

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

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

$y=c e^x-x$

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

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

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

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

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

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