Re: DSolve problems with system of ODEs. Out in pure notation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg21756] Re: DSolve problems with system of ODEs. Out in pure notation?*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Thu, 27 Jan 2000 22:56:38 -0500 (EST)*References*: <200001210900.EAA06601@smc.vnet.net> <200001220753.CAA11688@smc.vnet.net> <86e8o3$fbv@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

I have deleted the graphic display and most of the output. eqns = {x'[t] == -0.036 x[t] + 0.0124 y[t] + 0.000035 z[t] + 49.3, y'[t] == 0.0111 x[t] - 0.0286 y[t], z'[t] == 0.0039 x[t] - 0.000035 z[t], x[0] == 0, y[0] == 0, z[0] == 0}; soln = DSolve[ eqns, {x[t], y[t], z[t]}, t]; I am not sure what caused the error message. We can get what they indicate by Help Browser > GoTo [RootSum::pfn] with Other Information chosen from the category buttons. We get "Generated when the first argument in RootSum is not a Function expression." However it looks as if it is serious, since the solution is incorrect: soln /. t -> 0 {{x[0] -> 1.77331, y[0] -> -0.546333, z[0] -> -0.192132}} But, in reply to your question about the form of the answer: RootSum[f, form]represents the sum of form[x]for allx that satisfy the polynomial equationf[x] == 0. This is very useful notation - for mathematics in general, not just for Mathematica. In this case we can convert to standard notation (but it takes a while) ToRadicals[soln] And, with another wait, to traditional notation TraditionalForm[%] Since your input includes inexact numbers, you might accept the muchs shorter form. N[soln] Or maybe a numerical solution over some range of t (I have used -1 to 1) Numsoln = NDSolve[eqns, {x[t], y[t], z[t]}, {t, -1, 1}] This is OK at t=0: Numsoln /. t -> 0 {{x[0] -> 0., y[0] -> 0., z[0] -> 0.}} To check on the values throughout the t-range it is convenient to convert the solution to one for the functions x,y and z: FunNumsoln = Nsoln /. f_[t] -> f and, in eqns change Equal to Subtract: diffs = eqns /. Equal -> Subtract Now plot diffs with the functions substitued for x, y, z (with a perfect solution each would give constant zero function) Plot[Evaluate[diffs /. FunNumsoln], {t, -1, 1}, PlotRange -> All]; The maximum absolute error looks to be less than 0.000035. Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "J.Guillermo Sanchez" <guillerm at gugu.usal.es> wrote in message news:86e8o3$fbv at smc.vnet.net... > If I evaluate, > > DSolve[{x'[t] == -0.036 x[t] + 0.0124 y[t] + 0.000035 z[t] + 49.3, > y'[t] == 0.0111 x[t] - 0.0286 y[t], z'[t] == 0.0039 x[t] - 0.000035 > z[t], > x[0] == 0, y[0] == 0, z[0] == 0}, {x[t], y[t], z[t]}, t] > > I receive a massage like this > (RootSum::"pfn" : > "(DSolve`DSolveDump`dysfunction$6[273147 + <<1>>... > is not a pure function.). > and them a out in pure notation. > > But I want to receive the solution in standard notation. > > Also the same sentece work fine in Mathematica 2.2. > > Can anyone give a hand? > > > >

**References**:**Intersection of 2 subspaces***From:*RENAULT Fabien <renaulf1@cti.ecp.fr>

**Re: Intersection of 2 subspaces***From:*Daniel Lichtblau <danl@wolfram.com>