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