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Math Help - ODE--y''+(y')^2=2e^(-y)

  1. #1
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    ODE--y''+(y')^2=2e^(-y)

    Could someone help me solve this?

    y''+(y')^2=2e^{-y}

    So far I've got v\frac{dv}{dy}+v^2=2e^{-y} with v=y', which I also cannot solve.
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  2. #2
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    Quote Originally Posted by petition Edgecombe View Post
    Could someone help me solve this?

    y''+(y')^2=2e^{-y}

    So far I've got v\frac{dv}{dy}+v^2=2e^{-y} with v=y', which I also cannot solve.
    Divide by v and re-arrange to recognise that it's a Bernoulli DE: Bernoulli differential equation - Wikipedia, the free encyclopedia

    So make the substitution w = v^2.
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  3. #3
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    We haven't covered Bernoulli eqns yet, that's why I was stuck.
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