Differential Equations

$y+\frac{x^2 \tan ^{-1} x}{2}+\mathrm{c}=0$, where c is a constant of integration.

$y+x \tan ^{-1} x+\mathrm{c}=0$, where c is a constant integration.

$y-x-\tan ^{-1} x+\mathrm{c}=0$, where is a constant of integration.

$y=\frac{x^2 \tan ^{-1} x}{2}-\frac{1}{2}\left(x-\tan ^{-1} x\right)+\mathrm{c}$, where c is constant of integration.