Q:

How to solve this Diffrential equation?

$$ \frac{dy}{dx} = \frac{y+2}{x+1} + \tan\left(\frac{y-2x}{x+1}\right) $$
How can I turn it into a seperable differential equation? (I just want a hint).

A:

$y-2\,x=(y+2)-2(x+1)$. This suggests the change of variable $x+1=t$, $y+2=z$. The new equation is homogeneous.

