# Thread: homogeneous ODE requiring change of variables

1. ## homogeneous ODE requiring change of variables

dy/dx = (x - y + 2)/(x - y + 1)

i let x = X + p nad y = Y + q
then I have to solve what p and q are the only problem is when I use simulanteous equations both the p and q cancel out so I can't find what they equal.. =.= can anyone help?

2. Let u = x - y. Then u' = 1 - y'. The resulting DE is autonomous (no x's in it), hence separable.