       Re: Laplace Trasform system of differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg122062] Re: Laplace Trasform system of differential equation
• Date: Tue, 11 Oct 2011 04:24:41 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6rk79\$1oo\$1@smc.vnet.net> <j6uacn\$f1g\$1@smc.vnet.net>

```PlotStyle does work in ParametricPlot3D. There is no need to remove it.

Helen

On 10/10/2011 4:29 AM, Dr. Wolfgang Hintze wrote:
> "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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