       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)

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][] // 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 +
Sqrt[Pi]*BesselI[(-(1/2))*I*
Sqrt[15625*n^2 - 1], (1/2)*Sqrt[l^2 + m^2]*
(125*r + 2*z)]*C*Gamma[
1 - (1/2)*I*Sqrt[15625*n^2 - 1]]))/
2^(I*Sqrt[15625*n^2 - 1]))}

d = NestList[D[#, z] &, soln[], 2] // Simplify;

eqn[] /. 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.

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