       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 and C can be whatever you want...  In particular:

FullSimplify[DSolve[-y''[x] + Csc[x]^2*y[x] == y[x]/4, y[x], x]/.{C
-> a/(-1)^4^(-1), C -> 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  ArcTanh[Cos[x]]) (-5 a + Sqrt b
E^(Sqrt ArcTanh[Cos[x]])) Sqrt[Abs[Sin[x]]]}}

Simon

```

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