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Re: Wrong ODE solution in Mathematica 7?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106231] Re: Wrong ODE solution in Mathematica 7?
  • From: Alois Steindl <Alois.Steindl at tuwien.ac.at>
  • Date: Tue, 5 Jan 2010 01:49:28 -0500 (EST)
  • References: <hhshnt$kp4$1@smc.vnet.net>

Zsolt <phyhari at gmail.com> writes:

> 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?)
Hello,
what makes you think, that this solution is wrong?
You should know, that the same function can often be written in many
different ways.

To check the solution, you could simply compare the plots of its 2nd derivative
and the right hand side of the ODE or use TrigExpand[] on both functions
and their difference.

Alois


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