       Re: Laplace Trasform system of differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg122034] Re: Laplace Trasform system of differential equation
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Mon, 10 Oct 2011 04:26:45 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6rk79\$1oo\$1@smc.vnet.net>

```"elos" <marusik_92 at inbox.ru> schrieb im Newsbeitrag
news:j6rk79\$1oo\$1 at smc.vnet.net...
> 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 -> 1, y -> 1, z -> 1}
> sol2 = DSolve[{odeSys, x == 1, y == 1, z == 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]
>
Slight modifications of your code are sufficient for remedy

1) you need to use ParametricPlot3D
2) this function does not have the option PlotStle, so remove it

Hope this helps

Wolfgang

```

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