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Re: Wrong ODE solution in Mathematica 7?

• To: mathgroup at smc.vnet.net
• Subject: [mg106205] Re: Wrong ODE solution in Mathematica 7?
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Tue, 5 Jan 2010 01:44:16 -0500 (EST)
• References: <hhshnt$kp4$1@smc.vnet.net>

Zsolt wrote:

> 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! :)
>

There is no mistake, because the solutions are equivalent.

Mathematica solution:
f[x_]=C[1] + x*C[2] + (2*Sin[x/2])/(Cos[x/2] + Sin[x/2])

Other solution:
g[x_]= B + A*x - 2/(1 + Tan[x/2])

Comparison:
f[x]-g[x] //FullSimplify

Out= 2 - B - A x + C[1] + x C[2]

So the solutions are identical, supposed you choose A=C[2] and B=2+C[1]
as integration constants.

-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de