Re: Problem with symbolic solution of a differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg81608] Re: Problem with symbolic solution of a differential equation
• From: Mark Fisher <particlefilter at gmail.com>
• Date: Sat, 29 Sep 2007 02:27:34 -0400 (EDT)
• References: <fdi60t\$qff\$1@smc.vnet.net>

```On Sep 28, 2:12 am, Jepessen <jepes... at gmail.com> wrote:
> Hi to all.
>
> I've a problem with a differential equation, with Mathematica 6.0.1
> (Linux 32 bit)
>
> When I try to solve it simbolically, it returns me an error of
> indetermination.
>
> This is the equation
>
> eq = Derivative[2][f][t] + (2*l + m)*Derivative[1][f][t] +
>        l^2*f[t] == ((m + Sqrt[m*(4*l + m)])/(2*Sqrt[m*(4*l + m)]))*
>          Exp[(-(t/2))*((2*l + m) - Sqrt[m*(4*l + m)])] +
>        ((-m + Sqrt[m*(4*l + m)])/(2*Sqrt[m*(4*l + m)]))*
>          Exp[(-(t/2))*((2*l + m) + Sqrt[m*(4*l + m)])]
>
> This is the command that I use
>
> DSolve[{eq, f[0] == 0, Derivative[1][f][0] == 0}, f, t]
>
> and it returns me this error
>
> \[Infinity]::indet: "Indeterminate expression \
> ComplexInfinity+ComplexInfinity encountered. "
>
> So, I've tried to solve it numerically, and it works fine.
>
> fun = f /.
>   NDSolve[{Evaluate[eq /. {m -> .5, l -> .8}], f[0] == 0, f'[0] == 0},
>      f, {t, 0, 10}][[1]]
>
> Plot[fun[x], {x, 0, 10}]
>
> I obtain the right graph.
>
> I obviously know that there are equation that mathematica can't solve
> simbolically but, in these cases, it should return the unevaluated
> expression, instead of an error, especially considering that numerical
> method is fine.
>
> There's something that I can do to obtain a symbolic solution?
>
>
> Daniele Lupo

The following produces an answer in 6.0:

Assuming[m > 0, DSolve[{eq, Derivative[1][f][0] == 0, f[0] == 0}, f,
t]]

--Mark

```

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