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Re: New to mathematica: Question about solving
*To*: mathgroup at smc.vnet.net
*Subject*: [mg74694] Re: [mg74664] New to mathematica: Question about solving
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Sat, 31 Mar 2007 01:39:19 -0500 (EST)
*Reply-to*: hanlonr at cox.net
I must have evaluated out of order. Change this to read
soln=DSolve[{y'[x] == y[x] + y[x]^3}, y[x], x]
{{y[x] -> -((I*E^(x + C[1]))/
Sqrt[-1 + E^(2*x + 2*C[1])])},
{y[x] -> (I*E^(x + C[1]))/Sqrt[-1 + E^(2*x + 2*C[1])]}}
soln=soln/.
expr1_*(expr2_)^(-1/
2):>(expr2/(expr1^2))^(-1/2)/.C[1]:>-Log[C]/2//ExpandAll
{{y[x] -> 1/Sqrt[C/E^(2*x) - 1]},
{y[x] -> 1/Sqrt[C/E^(2*x) - 1]}}
Bob Hanlon
---- Bob Hanlon <hanlonr at cox.net> wrote:
> soln=DSolve[{y'[x] == y[x] + y[x]^3}, y[x], x]
>
> {{y[x] -> -((I*E^(x + C[1]))/
> Sqrt[-1 + E^(2*x + 2*C[1])])},
> {y[x] -> (I*E^(x + C[1]))/Sqrt[-1 + E^(2*x + 2*C[1])]}}
>
> soln=soln/.{
> expr1_*(expr2_)^(-1/2):>(expr2/(expr1^2))^(-1/2),
> C[1]:>-Log[C]/2}//ExpandAll
>
> {{y[x] -> 1/Sqrt[C/E^(2*x) - 1]},
> {y[x] -> 1/Sqrt[C/E^(2*x) - 1]}}
>
>
> Bob Hanlon
>
> ---- traz <t_raz at yahoo.com> 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?
> >
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