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