Re: Finding solutions to differential eqns
- To: mathgroup at smc.vnet.net
- Subject: [mg40107] Re: Finding solutions to differential eqns
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 21 Mar 2003 02:36:13 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <b5bjbn$5qp$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
can you use Mathematica's syntax to give an equation ?
And
DSolve[(2 x[t]*t*(1 - t))*x'[t] == 1 + x[t]^2, x[t], t] // FullSimplify
return
{{x[t] -> -Sqrt[-1 + (E^(2*C[1])*t)/(-1 + t)]},
{x[t] -> Sqrt[-1 + (E^(2*C[1])*t)/(-1 + t)]}}
In[]:=DSolve[x'[t] == (t/x[t])*Exp[x[t]/t] + x[t]/t, x[t], t] //
FullSimplify
Out[]={{x[t] -> -(t*(1 + ProductLog[(C[1] + Log[t])/E]))}}
In[]:=DSolve[x'[t] == (t - 4)*Exp[ 4 t] + t *x[t], x[t], t] //
FullSimplify
Out[]={{x[t] -> -E^(4*t) + E^(t^2/2)*C[1]}}
Regards
Jens
David wrote:
>
> Is there a method where you can get Mathematica to find general
> solutions for differential equations? For example:
>
> [2xt(1 + t)]dx/dt = 1 + x^2
>
> dx/dt = (t/x)e^(-x/t) + x/t
>
> and
>
> dx/dt = (t - 4)e^4t + tx
>
> I have access to version 4.0
>
> Cheers,
>
> David