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Re: Help on 3rd order nonlinear ode


Jay wrote:

> I tried to solve the following third order nonlinear ode using NDSolve
> in Mathematica:
>
> (y'[x])^2 + y[x]*y''[x] + 10*  y'''[x] == 10
>
> with boundary/initial conditions
>
> y[0] == 0, y'[0] == 0, y'[10] == 1.
>
> However, Mathematica says:
>
> NDSolve::"pcnan": "Coefficients of the differential equation are not
> numbers \ or only one linear nth order ordinary differential equation
> can be solved."
>
> Can you help me please?
>
> Thanks,
> Jay

    The LHS of your eq. is (y[x]^2+20y[x]')''/2 . Therefore, the solution
to your equation can be obtained from the solutions of the first order
ode:

y[x]^2+20y[x]'=10x^2+2a x +b, for arbitrary constants a,b.

Your boundary conditions imply b=0, but do not determine a. You must know
y[0]'' to determine a.

Good luck!
SB



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