I understand that if I have a differential equation that I can write in the form of
$$ A(x,y)dx+B(x,y)dy=0 $$
, where $A(x,y)$ and $B(x,y)$ are both homogenous functions of the same degree, then I proved the equation is homogenous of that degree.
I can easily prove that functions are homogenous of degree 0.
However, in the following equation I could not make if of the form $A(x,y)dx+B(x,y)dy=0$ for some reason.
The equation in question is:
$$ dy/dx=e^{y/x}+y/x $$
I tried moving $dy/dx$ over to the right side of the equation, however I ended up with $e^{y/x}*dx/dy+y/x*dx/dy=0$.
How do I put in the form of $A(x,y)dx+B(x,y)dy=0$?