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Re: New to mathematica: Question about solving differential eqs
*To*: mathgroup at smc.vnet.net
*Subject*: [mg74675] Re: New to mathematica: Question about solving differential eqs
*From*: Roger Bagula <rlbagula at sbcglobal.net>
*Date*: Sat, 31 Mar 2007 01:27:14 -0500 (EST)
*References*: <euig8p$otm$1@smc.vnet.net>
traz wrote:
>Whenever I try to solve differential equations in mathematica, I get a solution with an imaginary part different from the solution in a text book. For example:
>
>DSolve[{y'[x] == y[x] + y[x]^3}, y, x]
>
>will give me a solution that has an imaginary part and not the one I expect here from the text book:
>
>{+(Ce^(-2x)-1)^(-1/2), -(Ce^(-2x)-1)^(-1/2)}
>
>Can anyone give me a tip on how to do this? Also does anyone know of an online tuttorial that goes into details a little bit?
>
>
>
dy/dx=y+y^3
rearranging:
dx=dy/(y+y^3)
Solving for x in terms of y ( instead of y in terms of x):
x=Integrate[1/(y + y^3), {y, a, ya}]
You'll see that give two alternative solutions for the variable x
which are dependent on the actual value of y.
If you chose the one solution:
x=-(2*Log[a]-Log[1+a^2]-2*Log[y]+Log[1+y^2])/2
Solve[x == -(2*Log[a] - Log[1 + a^2] - 2*Log[y] + Log[1 + y^2])/2, y]
gives the answers that I think you are looking for.
The two solutions seem to be the same depending on the values of the
constants.
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