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Re: DSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83177] Re: DSolve
  • From: dh <dh at metrohm.ch>
  • Date: Wed, 14 Nov 2007 04:42:13 -0500 (EST)
  • References: <fhc3n2$4vv$1@smc.vnet.net>


Hi Ray,

there is no doubt that u[x]==0 is a solution.

But are there other solutions? To answer this consider: u''=-\[Lambda]^2 

(0.25 - x^2) u[x]. This means that between [-0.5,0.5] where (0.25 - x^2) 

is positive, the right side of the equation is - pos u[x] where pos is a 

positive expression. This means that for u!=0 the curve bends towards 

the x-axis. If \[Lambda] is larger, this effect is stronger. Therefore, 

starting at x=-1/2 with a given slope, the curve hits u[1/2]==0 only for 

very special values of \[Lambda].

Shortly, the generic solution is u[x]==0, other solutions are only 

possible for special values of \[Lambda].

hope this helps, Daniel



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

> 

> 




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