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Question: How can I get a simple solution out of pdsolve ? 

Question:How can I get a simple solution out of pdsolve ? 

WouterSe 15 Maple
syntax pde pdsolve differential-equations
October 07 2019
3

 

pdsolveComesUpWithComplexResult.mw

I'm struggling to get a simple answer out of pdsolve solving this PDE:  

eqn := Mu*diff(`ξr`(r, t), t, t) = kappa*diff(`ξr`(r, t), r, r);
ic := `ξr`(r, 0) = sin(Pi/(2*r)), D[2](`ξr`)(r, 0) = 0;
bc := `ξr`(0, t) = 0, D[1](`ξr`)(1, t) = 0;
sol := (pdsolve([eqn, ic, bc], Zeta(r, t)) assuming (0 < kappa, 0 < Mu));

The outcome pdsolve comes up with is rather complex, with summation and integral. To my best knowledge, the simple solution of this PDE is:

sin(Pi*r/2)*cos(1/2*sqrt(k/m)*Pi*t)

How can I get this simple solution out of pdsolve? 

Any suggestion is welcome.

Wouter
 
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