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.