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] == 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