       Re: Solving a DE using Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg90452] Re: Solving a DE using Mathematica
• From: dh <dh at metrohm.ch>
• Date: Thu, 10 Jul 2008 06:32:33 -0400 (EDT)
• References: <g51uce\$6tj\$1@smc.vnet.net>

```
Hi Greg,

how do you determine that the solution stuffed into the equation is not

zero?? First, simplify your equation. constant^2 is still constant. l^2

+ m^2 is still constant n^2/(r+0.016 z) may be written c1(c2+z). Therefore:

eq=(m+n/(r+ z)^2) Z[z]+Z''[z]==0;

sol=DSolve[eq,Z,z]

now is this a solution?

eq /. sol // Simplify

does not answer the question, Mathematica can  not decide if it is True. I think

the Whittacker functions  are the Problem. What can we do? The simpliest

is to do some numerical tests. E.g.:

eq /. sol  /. {m -> 1, n -> 3, r -> 7, z -> I} // Simplify // N

stuff in some other numbers. I, at least, always get zero to numerical

accuracy. Sure, you can not be certain it really is zero. But by trying

enough you may increase the probability that it is.

hope this helps, Daniel

Greg 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.

>

--

Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>

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