How do I solve this one?

(2x - y + 4)dy + (x - 2y + 5)dx = 0

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- Sep 12th 2011, 08:14 PMmafraFirst-order nonlinear ordinary differential equation
How do I solve this one?

(2x - y + 4)dy + (x - 2y + 5)dx = 0 - Sep 12th 2011, 08:20 PMalexmahoneRe: First-order nonlinear ordinary differential equation
$\displaystyle \frac{dy}{dx}=\frac{2y-x-5}{2x-y+4}$

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 $\displaystyle 2x-y+4=2u-v+4$.