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Re: question about ndsolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131661] Re: question about ndsolve
  • From: rchagw at gmail.com
  • Date: Tue, 17 Sep 2013 21:34:53 -0400 (EDT)
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On Tuesday, September 10, 2013 3:24:43 AM UTC-4, Hagwood, Charles R wrote:
> I know the following differential equation has a solution, but cannot get NDSolve to find it.
> 
> 
> 
> 
> 
> dgamma[s_,a_]:=1+9.6*(s-1)^2*s+9.6*s^2*(s-1)
> 
> q2[x_]:=Sqrt[2*Pi]*{-Sin[2*Pi*x],Cos[2*Pi*x]}
> 
> q1[x_,a_]:=Sqrt[2*Pi*dgamma[x,a]]*{-Sin[2*Pi*gamma[x,a]],Cos[2*Pi*gamma[x,a]]}
> 
> 
> 
> 
> 
> h1[x_]:=q2[x].q2'[x]
> 
> h2[x_]:=q2[x].q2[x]
> 
> 
> 
> 
> 
> sol=NDSolve[{-6*y'[x]^2*(q1[x,.3].q2'[y[x]]) +6*y'[x]^(5/2)*h1[y[x]]+y''[x]*(q1[x,.3].q2[y[x]])-y''[x]*y'[x]^(1/2)*h2[y[x]]==0,y[0]==0,y[1]==1},y,{x,0.01,1},Method->{"Shooting","StartingInitialConditions"->{y[0]==0}}]
> 
> 
> 
> I get the error  NDSolve::ntcs: Cannot solve constraint equations for initial conditions. <http://reference.wolfram.com/mathematica/ref/message/NDSolve/ntcs.html> 
> 
> 
> 
> 
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> The solution is
> 
> 
> 
> y[x_]:=x+16*a*x^2*(x-1)^2
> 
> a=.3;
> 
> 
> 
> The following expression is zero for all values of x
> 
> 
> 
> -6*y'[x]^2*(q1[x,.3].q2'[y[x]]) +6*y'[x]^(5/2)*h1[y[x]]+y''[x]*(q1[x,.3].q2[y[x]])-y''[x]*y'[x]^(1/2)*h2[y[x]]/.x->.9
> 
> 
> 
> 
> 
> Does anyone know what is going wrong with NDSolve?
> 
> 
> 
> Charles Hagwood

gamma[s_,a_]:=s+16*a*s^2*(s-1)^2



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