Re: Wrong ODE solution in Mathematica 7?

*To*: mathgroup at smc.vnet.net*Subject*: [mg106194] Re: [mg106177] Wrong ODE solution in Mathematica 7?*From*: "Tony Harker" <a.harker at ucl.ac.uk>*Date*: Tue, 5 Jan 2010 01:42:00 -0500 (EST)*References*: <201001041058.FAA21179@smc.vnet.net>

Let Mathematica check it: eq = D[y[x], x, x] == -Cos[x]/(1 + Sin[x])^2 sol = DSolve[eq, y, x] eq /. sol[[1]] // Simplify returns True. So the solution is correct, and if you think about it the difference between Mathematica's solution and the other one is only a matter of a difference in the additive constant. Tony ]-> -----Original Message----- ]-> From: Zsolt [mailto:phyhari at gmail.com] ]-> Sent: 04 January 2010 10:59 ]-> To: mathgroup at smc.vnet.net ]-> Subject: [mg106177] Wrong ODE solution in Mathematica 7? ]-> ]-> 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! :) ]-> ]->

**References**:**Wrong ODE solution in Mathematica 7?***From:*Zsolt <phyhari@gmail.com>