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Math Help - First-Order ODE

  1. #1
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    Question First-Order ODE

    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?
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  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
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    near Piacenza (Italy)
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    Re: Find a solution to a differential equation

    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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