• To: mathgroup at smc.vnet.net
• Subject: [mg131598] question about ndsolve
• From: "Hagwood, Charles R" <charles.hagwood at nist.gov>
• Date: Tue, 10 Sep 2013 03:34:27 -0400 (EDT)
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```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>

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

```

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