Re: DSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg83175] Re: DSolve
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 14 Nov 2007 04:41:05 -0500 (EST)
- Organization: Uni Leipzig
- References: <fhc3n2$4vv$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
Hi,
from
eqn = D[u[x], {x, 2}] + \[Lambda]^2 (1/4 - x^2) u[x] == 0;
sol = DSolve[eqn, u[x], x]
you see that Mathematica find a solution
ins = eqn /. Flatten[{#, D[#, x], D[#, {x, 2}]} & /@ sol[[1]]] //
FullSimplify
gives not zero, but
ins /. x -> 2. /. \[Lambda] -> -1.
show you that Mahematica has found a solution.
But it find no
solution for the boundary conditions you gave can't be satisfyed
because from:
s1 = 0 == (u[x] /. sol[[1]]) /. x -> -1/2;
s2 = 0 == (u[x] /. sol[[1]]) /. x -> 1/2;
{s1, s2} /. \[Lambda] -> -2 // N
you see that C[1] must be zero becaus the ParabolicCylinderD[] function
is complex and this gives that also C[2] must be zero too
Regards
Jens
Raj wrote:
> eqn = D[u[x], {x, 2}] + \[Lambda]^2 (0.25 - x^2) u[x] == 0
> DSolve[{eqn, u[-1/2] == 0, u[1/2] == 0}, u[x], x]
>
> This returns {{u[x] -> 0}} while another CAS system returns a solution
> in terms of WhittakerW function.
>
> Am I doing something wrong or is Mathematica not able to solve this
> equation symbolically?
>
> Thanks,
>
> Raj
>
>