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Re: mathematica gives strange result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111313] Re: mathematica gives strange result
  • From: Simon <simonjtyler at gmail.com>
  • Date: Tue, 27 Jul 2010 04:17:36 -0400 (EDT)
  • References: <i2gjom$3m$1@smc.vnet.net> <i2h86h$2hd$1@smc.vnet.net>

> It suprised me because the solution isn't real, i'm looking for real
> one, but mathematica gives me onle this.

It's a linear ODE, so all solutions are a linear combination of two
basis solutions. This means that the automatically generated constants
C[1] and C[2] can be whatever you want...  In particular:

FullSimplify[DSolve[-y''[x] + Csc[x]^2*y[x] == y[x]/4, y[x], x]/.{C[1]
-> a/(-1)^4^(-1), C[2] -> b/(-1)^4^(-1)},Element[x, Reals]]

yields a solution (which for real a and b) is manifestly real:

{{y[x] -> -(1/5) E^(-(1/2) Sqrt[5]  ArcTanh[Cos[x]]) (-5 a + Sqrt[5] b
E^(Sqrt[5] ArcTanh[Cos[x]])) Sqrt[Abs[Sin[x]]]}}

Simon


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