# Question:phaseportrait of a differential equation

## Question:phaseportrait of a differential equation

Maple

Hi all

> deq := diff(theta(t), t, t)+g*sin(theta(t))/L = 0;

/  2          \
| d           |   g sin(theta(t))
deq := |---- theta(t)| + --------------- = 0
|   2         |          L
\ dt          /
> g, L := 9.8, 1;

g, L := 9.8, 1
> ci := theta(0) = (1/2)*Pi, (D(theta))(0) = 0;

1
ci := theta(0) = - Pi, D(theta)(0) = 0
2
> p := dsolve({ci, deq}, type = numeric, range = 0 .. 10);

p := proc(x_rkf45)  ...  end;
> p(3);

[                                           d                                 ]
[t = 3., theta(t) = -0.170858323972852610, --- theta(t) = -4.39484726433572170]
[                                           dt                                ]

>plots[odeplot](p,numpoints=1000)

But I would like to plot D(theta)(t) versus theta(t).  It seems that it could not be done with

> with(DEtools);
> phaseportrait(deq, (D(theta))(t), t = 0 .. 10, [[ci]], theta = -Pi/2 .. Pi/2, stepsize = 0.5e-1);

Any ideas?

Mario

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