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Troubles with NDSolve--missing arguments of function

• To: mathgroup at smc.vnet.net
• Subject: [mg81041] Troubles with NDSolve--missing arguments of function
• From: "lederer at ssb.rochester.edu" <lederer at ssb.rochester.edu>
• Date: Sun, 9 Sep 2007 06:11:14 -0400 (EDT)

I am having a problem with NDSolve.  I am trying to solve a two
function- calculus of variations problem by solving a system of
differential equations. Here is a simplified description of my current
troubles, reducing the equations for the problem to one function,
b[x], b'[x], defined on a closed interval on the real line.

When applying NDSolve, Mathematica  keeps giving me a message saying
that =E2=80=9Cb=E2=80=9D --- is missing its parameter.

This is where I think it is coming from:  As one of constraints I have
something like:

=E2=88=82f[b,b=E2=80=99[x],x]/=E2=88=82b  *  db[x]/dx==0  with the expression evaluated at
b=b[x]

that is,  my constraint is:  the partial derivative of the function
f=E2=80=99s  first argument evaluated at b[x] and then multiplied by the
derivative of b[x] wrt x=E2=80=A6.. and is set to zero.

The way I am doing this in Mathematica is

( D[f[b,b'[x], x],b]/.b->b[x]  )*D[b[x],x]==0

I think the program is upset that the left hand side of one of the
constraints has a function =E2=80=9Cb=E2=80=9D without its usual argument, b[x]

But if I try:

 D[   f[ b[x],b'[x],x]  ,   x  ] I will get the complete derivative
of f wrt x which is just plain wrong.

Two related questions:

How can I get the constraint I want?      and/or

Is what I am doing correct,  but my diagnosis of the error message is
(likely) wrong?

Many thanks in advance.

Phil