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Re: non-linear equations not covered by built-in procedures

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38832] Re: [mg38809] non-linear equations not covered by built-in procedures
  • From: "Bobby R. Treat" <majort at cox-internet.com>
  • Date: Wed, 15 Jan 2003 02:19:51 -0500 (EST)
  • References: <200301141110.GAA26240@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Using version 4.2, I get various error messages (not the one you mentioned) 
, but a correct solution is found anyway.

eqn = Derivative[2][r][t] + 1/r[t] == 0; DSolve[{eqn, r[0] == 1, 
Derivative[1][r][0] == 0}, r[t], t]
soln[t_] = r[t] /. Last[%]; Plot[soln[t], {t, 0, Sqrt[Pi/2]}]

{{r[t] -> E^(-InverseErf[0, (-Sqrt[2/Pi])*t]^2)}, {r[t] -> E^(- 
InverseErf[0, Sqrt[2/Pi]*t]^2)}}

Bobby

On Tue, 14 Jan 2003 06:10:37 -0500 (EST), Narasimham G.L. 
<mathma18 at hotmail.com> 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
>
>
>



-- 
majort at cox-internet.com
Bobby R. Treat



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