Re: Wrong ODE solution in Mathematica 7?

*To*: mathgroup at smc.vnet.net*Subject*: [mg106227] Re: [mg106177] Wrong ODE solution in Mathematica 7?*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 5 Jan 2010 01:48:40 -0500 (EST)*Reply-to*: hanlonr at cox.net

The arbitrary constants between the two are different. eqn = D[y[x], x, x] == -Cos[x]/(1 + Sin[x])^2; soln1 = DSolve[eqn, y[x], x][[1, 1]] y[x] -> C[2]*x + C[1] + (2*Sin[x/2])/(Sin[x/2] + Cos[x/2]) D[y[x] /. soln1, x, x] == (eqn // Last) // Simplify True The solution satisfies the equation. soln2 = (y[x] -> -2/(Tan[(1/2)*x] + 1) + C[4]*x + C[3]); Series[Evaluate[y[x] /. soln1], {x, 0, 1}] // Normal (C[2] + 1)*x + C[1] Series[Evaluate[y[x] /. soln2], {x, 0, 1}] // Normal (C[4] + 1)*x + C[3] - 2 (y[x] /. soln1) == (y[x] /. soln2 /. {C[3] -> C[1] + 2, C[4] -> C[2]}) // Simplify True The solutions are equivalent. Bob Hanlon ---- Zsolt <phyhari at gmail.com> 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! :)