       Problem with symbolic solution of a differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg81574] Problem with symbolic solution of a differential equation
• From: Jepessen <jepessen at gmail.com>
• Date: Fri, 28 Sep 2007 02:09:17 -0400 (EDT)

```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[f][t] + (2*l + m)*Derivative[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, Derivative[f] == 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, f' == 0},
f, {t, 0, 10}][]

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?