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Math Help - Help for the solution of nonlinear differential equation:y"+(y')^2+y=0

  1. #1
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    Smile Help for the solution of nonlinear differential equation:y"+(y')^2+y=0

    Hi,
    Can you help me to found an analytical solution of:
    d2x/dt^2+ c1 (dx/dt)^2+ c2x=0

    Thanks
    Mike
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    If a differential equation has the form

    F(y,y',y'')=0\quad[*]

    the substitution:

    y'=p,\quad (p=p(y))

    transforms [*] into:

    F\left(y,p,p\dfrac{dp}{dy}\right)=0

    (first order equation).


    Fernando Revilla
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