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Re: DSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83266] Re: [mg83169] DSolve
  • From: "W. Craig Carter" <ccarter at mit.edu>
  • Date: Fri, 16 Nov 2007 05:35:04 -0500 (EST)
  • References: <200711131200.HAA05087@smc.vnet.net>

> 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

Dear Raj,

Math6 will find a solution in terms of ParabolicCylinderD 
for undetermined coefficients. This function and WhittikerW 
are related to the Hypogeometric functions. I can't see why 
your extra conditions are giving a zero: 
ParabolicCylinderD has zeroes for real lambda. Perhaps you 
will have to find the eigenvalues, lambda, with a rootsolver 
for ParabolicCylinderD.

Trying Assuming[\[Lambda] \[Element] Reals, DSolve[{eqn}, 
u[x], x]]




  • References:
    • DSolve
      • From: Raj <rajanikanth@gmail.com>
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