Differential Equations

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

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

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

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