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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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