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Wrong ODE solution in Mathematica 7?

• To: mathgroup at smc.vnet.net
• Subject: [mg106177] Wrong ODE solution in Mathematica 7?
• From: Zsolt <phyhari at gmail.com>
• Date: Mon, 4 Jan 2010 05:58:48 -0500 (EST)

Hi!
I tried solve the ODE:
DSolve[D[y[x], x, x] == -Cos[x]/(1 + Sin[x])^2, y[x], x]

The solution what M7 (and Wolfram Alpha) gives is:
y[x] -> C[1] + x C[2] + (2 Sin[x/2])/(Cos[x/2] + Sin[x/2])

I think, it's wrong! (Does anybody know how to check?) Another system gives
for the same diff.eq:
y(x) = -2/(tan((1/2)*x)+1)+_C1*x+_C2
(similar, but not the same->ctan vs tan...)
I found the problem in one of my math books, and the solution there
concours with the other system.
How can I trust Mathematica, if it makes mistakes in such simple
things?? :(
Thank you for your answer! :)

• Follow-Ups:
  • Re: Re: Wrong ODE solution in Mathematica 7?
    • From: DrMajorBob <btreat1@austin.rr.com>
  • Re: Wrong ODE solution in Mathematica 7?
    • From: Murray Eisenberg <murray@math.umass.edu>
  • Re: Wrong ODE solution in Mathematica 7?
    • From: Leonid Shifrin <lshifr@gmail.com>
  • Re: Wrong ODE solution in Mathematica 7?
    • From: DrMajorBob <btreat1@austin.rr.com>
  • Re: Wrong ODE solution in Mathematica 7?
    • From: "Tony Harker" <a.harker@ucl.ac.uk>