dy/dx = x+y, I am suppose to solve using the substitution: u=x+y
I'm really confused by this one, I don't even know where to start. Anyone?
Yes, that's prabably the easiest way.
$\displaystyle u = x + y$ so $\displaystyle \frac{du}{dx} = \frac{dy}{dx} + 1$ so your DE becomes $\displaystyle \frac{du}{dx} = u + 1$ which is separable.