       Re: Help on 3rd order nonlinear ode

• To: mathgroup at smc.vnet.net
• Subject: [mg28337] Re: Help on 3rd order nonlinear ode
• From: Sotirios Bonanos <sbonano at mail.ariadne-t.gr>
• Date: Thu, 12 Apr 2001 02:18:01 -0400 (EDT)
• Organization: National Technical University of Athens, Greece
• References: <9b0sut\$rs@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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, y' == 0, y' == 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'' to determine a.

Good luck!
SB

```

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