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

**manvalan** · January 16th 2011, 11:54 PM

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

Thanks
Mike

**FernandoRevilla** · January 17th 2011, 01:14 AM

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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