Re: Solving a DE using Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg90483] Re: [mg90424] Solving a DE using Mathematica*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Thu, 10 Jul 2008 06:38:31 -0400 (EDT)*Reply-to*: hanlonr at cox.net

eqn = Rationalize[(-l^2 - m^2 + n^2/(r + 0.016 z)^2) Z[z] + Z''[z] == 0, 0]; soln = DSolve[eqn, Z[z], z][[1]] // FunctionExpand // Simplify {Z[z] -> (1/Sqrt[Pi])* ((Sqrt[Sqrt[l^2 + m^2]*(125*r + 2*z)]* (2^(I*Sqrt[15625*n^2 - 1])*BesselK[ (-(1/2))*I*Sqrt[15625*n^2 - 1], (1/2)*Sqrt[l^2 + m^2]*(125*r + 2*z)]*C[2] + Sqrt[Pi]*BesselI[(-(1/2))*I* Sqrt[15625*n^2 - 1], (1/2)*Sqrt[l^2 + m^2]* (125*r + 2*z)]*C[1]*Gamma[ 1 - (1/2)*I*Sqrt[15625*n^2 - 1]]))/ 2^(I*Sqrt[15625*n^2 - 1]))} d = NestList[D[#, z] &, soln[[1]], 2] // Simplify; eqn[[1]] /. d // FullSimplify 0 eqn /. d // FullSimplify True Bob Hanlon ---- Greg <starwar636 at aol.com> wrote: ============= I'm having problems solving this problem although it should appear pretty straightfoward: (-l^2 - m^2 + n^2/(r + 0.016 z)^2) Z[z] + Z''[z] == 0 I am solving for Z[z]. These are the lines I use: DSolve[Above Equation, Z[z], z] I get an odd solution so I do a solution check plugging back in Z[z] and Z''[z] yet I don't get 0. In the above, l,m,n,r are all constants.