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