       Re: New to mathematica: Question about solving

• To: mathgroup at smc.vnet.net
• Subject: [mg74692] Re: [mg74664] New to mathematica: Question about solving
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 31 Mar 2007 01:38:17 -0500 (EST)

```soln=DSolve[{y'[x] == y[x] + y[x]^3}, y[x], x]

{{y[x] -> -((I*E^(x + C))/
Sqrt[-1 + E^(2*x + 2*C)])},
{y[x] -> (I*E^(x + C))/Sqrt[-1 + E^(2*x + 2*C)]}}

soln=soln/.{
expr1_*(expr2_)^(-1/2):>(expr2/(expr1^2))^(-1/2),
C:>-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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