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? > > Thanks for answers > > 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