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>
• 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
>