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Re: NIntegrate and NDSolve


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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