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Laplace Trasform system of differential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122022] Laplace Trasform system of differential equation
  • From: elos <marusik_92 at inbox.ru>
  • Date: Sun, 9 Oct 2011 03:53:07 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

where I made a mistake? I need to solve the system of differential equations using Laplace transforms and the plots. Solve happened, but no graphics.


odeSys = {x'[t] - x[t] + y[t] == 0,
                 y'[t] - x[t] - y[t] == 0, 
                 z'[t] - x[t] - y[t] - 2*z[t] == 0}
eq1 = LaplaceTransform[odeSys, t, s]
eq2 = Solve[eq1, {LaplaceTransform[x[t], t, s],
                             LaplaceTransform[y[t], t, s], 
                             LaplaceTransform[z[t], t, s]}]
sol1 = Map[InverseLaplaceTransform
     [#, s, t] &, eq2, {3}] /. {x[0] -> 1, y[0] -> 1, z[0] -> 1}
sol2 = DSolve[{odeSys, x[0] == 1, y[0] == 1, z[0] == 1},
   {x[t], y[t], z[t]}, t] // Simplify
ParametricPlot[Evaluate[{x[t], y[t], z[t]} /. sol1],
 {t, 0, 1}, PlotStyle -> {Hue[0.5], Thickness[0.01]}]


Here is system of differential equations: x'[t]=x[t]-y[t]
                                                                y'[t]=x[t]+y[t]
                                                              z'[t]=x[t]+y[t]+2*z[t]



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