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