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Re: Wrong ODE solution in Mathematica 7?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106193] Re: Wrong ODE solution in Mathematica 7?
*From*: dh <dh at metrohm.com>
*Date*: Tue, 5 Jan 2010 01:41:49 -0500 (EST)
*References*: <hhshnt$kp4$1@smc.vnet.net>
Hi,
both are correct. You may check this by calculating the second
derivative of both expressions and show that they are equal:
D[-2/(Tan[(1/2)*x] + 1), {x, 2}] ==
D[(2 Sin[x/2])/(Cos[x/2] + Sin[x/2]), {x, 2}] // Simplify
Daniel
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! :)
>
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