Differential Equations

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

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

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

$\log \left|\frac{\sin (x-y)+\cos (x-y)}{\cos (x-y)}\right|=x+C$