I am reading a book about differential equations and I found this equation in the chapter about homogeneous differential equations. The books solves this equation by turning it to a homogeneous.
This reminds me the kind of equation that can be solved this way.
$M(x,y) = x + y -1$ $N(x,y) = x-y+1$
$M_{y} = 1$ $N_{x} = 1$
so $\phi (x,y) = \int_{0}^{x}t+y-1 dt +\int_{0}^{y} -t -1 dt$
Is this thought correct?