First-Order ODE

**paroxsitic** · September 21st 2011, 07:12 AM

Diff. Eq.:
$x{\it dy}- \left( 2\,{{\it xe}}^{-{\frac {y}{x}}}+y \right) {\it dx}=0$
Initial Condition:
y(1)=0

I don't see any way to get all the x and dx on one side and the y dy on the other. I assume the only way to do this is using the initial condition x=1 and y=0 to eliminate some of the variables before it is simplified?

**chisigma** · September 21st 2011, 08:07 AM

Write the DE in a little different way...

$\frac{dy}{dx}= 2\ e^{-\frac{y}{x}}+\frac{y}{x}$ (1)

... and the set...

$z=\frac{y}{x} \implies \frac{dy}{dx}= z + x\ \frac{dz}{dx}$ (2)

Kind regards

$\chi$ $\sigma$

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