Re: non-linear equations not covered by built-in procedures
- To: mathgroup at smc.vnet.net
- Subject: [mg38828] Re: non-linear equations not covered by built-in procedures
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 15 Jan 2003 02:19:32 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <b00rgm$pmb$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
a) my Mathematica 4.2 can solve it
b) it's simple to solve it by hand with
eqn = r''[t] + 1/r[t] == 0;
st1 = Solve[((Integrate[#1, {t, 0, \[Tau]}] & ) /@
Expand[Derivative[1][r][t]*#1] & ) /@ eqn /.
{r[0] -> 1, Derivative[1][r][0] -> 0},
Derivative[1][r][\[Tau]]] /. Rule -> Equal;
Solve[\[Tau] == Integrate[1/#, r[\[Tau]]], r[\[Tau]]] & /@
Last /@ Flatten[st1]
Regards
Jens
"Narasimham G.L." wrote:
>
> Hi,
>
> I am a beginner with Mathematica. Apprecite help for non-linear
> diffrl. equns.
>
> eqn = r''[t] + 1/r[t] == 0
> sol = DSolve[{eqn, r[0] == 1, r'[0] == 0}, r[t], t]
> Plot[r[t] /. sol, {t, 0, 2Pi }]
>
> carries error msg >> DSolve::dnim:
> Built-in procedures cannot solve this differential equation.
>
> The linear case when 1/r[t] is replaced by r[t] works OK,yields the
> expected Cos[t] solution.
> Is there a web accessible Mathematica reference for ODEs, non linear,
> PDEs etc.?
>
> Regards