First-order nonlinear ordinary differential equation

**mafra** · September 12th 2011, 08:14 PM

How do I solve this one?

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

**alexmahone** · September 12th 2011, 08:20 PM

Originally Posted by mafra

How do I solve this one?

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

$\frac{dy}{dx}=\frac{2y-x-5}{2x-y+4}$

Let $x=u+h$ and $y=v+h$ , where $h$ and $k$ are constants that are to be determined.

$dx=du$ and $dy=dv$

We want $\frac{dv}{du}=\frac{2v-u}{2u-v}$ , so that we have a homogeneous equation, that can be easily solved.

Find $h$ and $k$ by setting $2y-x-5=2v-u$ and $2x-y+4=2u-v+4$ .

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