Re: NIntegrate and NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg56527] Re: NIntegrate and NDSolve
• From: Peter Pein <petsie at arcor.de>
• Date: Thu, 28 Apr 2005 02:40:15 -0400 (EDT)
• References: <d4mrmq\$1st\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Matt Flax wrote:
> Hello,
>
> I have an equation which depends on the integral and differential
> of an unknown function f[x,y,z].
>
> I would like to solve this equation analytically, however am happy with a
> numerical solution if that is necessary.
>
> The equation contains the unknown (f[x,y,z]) which I would like to solve
> for and has integrals of differentials like this :
>
> Integral [ d f[x,y,z] / dz  , dx]
> Integral [ d f[x,y,z] / dx  , dz]
>
>
> It is set up like this :
>
> (Integral [ d f[x,y,z] / dz  , dx] )(knownTrigPoly1[y]) +
> (Integral [ d f[x,y,z] / dx  , dz] )(knownTrigPoly2[y]) == 0
>
> Any I would like to solve for f[x,y,z] (numerically if necessary).
>
> Can anyone let me know how to use DSolve or another function to solve
> this equation for f[x,y,z] ?
>
> thanks
> Matt
Hi Matt,

I would try:

eq = ( Integrate[D[f[x, y, z], z], x]*p1[y] +
Integrate[D[f[x, y, z], x], z]*p2[y] ) == 0;
DSolve[D[eq, x, z], f, {x, y, z}]
Out[2]=
{{f -> Function[{x, y, z},
C[1][y][z + (x*Sqrt[(-p1[y])*p2[y]])/p2[y]] +
C[2][y][z - (x*Sqrt[(-p1[y])*p2[y]])/p2[y]] ]}}

Simplify[eq/.%[[1]]]
Out[3]=
True
--
Peter Pein
Berlin

```

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