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