Re: Re: Wrong ODE solution in Mathematica 7?
- To: mathgroup at smc.vnet.net
- Subject: [mg106243] Re: [mg106194] Re: [mg106177] Wrong ODE solution in Mathematica 7?
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Wed, 6 Jan 2010 05:58:26 -0500 (EST)
- References: <201001041058.FAA21179@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
Actually, the difference is a constant plus another constant times x. Bobby On Tue, 05 Jan 2010 00:42:00 -0600, Tony Harker <a.harker at ucl.ac.uk> wrote: > 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! :) > ]-> > ]-> > > -- DrMajorBob at yahoo.com
- References:
- Wrong ODE solution in Mathematica 7?
- From: Zsolt <phyhari@gmail.com>
- Wrong ODE solution in Mathematica 7?