How do I solve this one?
(2x - y + 4)dy + (x - 2y + 5)dx = 0
$\displaystyle \frac{dy}{dx}=\frac{2y-x-5}{2x-y+4}$
Let $\displaystyle x=u+h$ and $\displaystyle y=v+h$, where $\displaystyle h$ and $\displaystyle k$ are constants that are to be determined.
$\displaystyle dx=du$ and $\displaystyle dy=dv$
We want $\displaystyle \frac{dv}{du}=\frac{2v-u}{2u-v}$, so that we have a homogeneous equation, that can be easily solved.
Find $\displaystyle h$ and $\displaystyle k$ by setting $\displaystyle 2y-x-5=2v-u$ and $\displaystyle 2x-y+4=2u-v+4$.