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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>