How could I adjust that to see what happens for negative time? Perhaps through in animation.

Thanks, that's better than what I got from this thread:

http://www.mapleprimes.com/forum/phaseportrait#comment-14266

Nevermind delete this thread.

And if I wanted to write a conditional statement

If the eigenvalues are real and have opposite signs

Print Saddle Point

else If eigenvalues are both real with same sign

print node

else if eigenvalues are both real with complex conjugate

print spirals

else if at least one of the eigenvalues is zero

print not an isolated fixed point

end

end

end

My issue is how would I get make to look at each eigenvalue for the above conditions?

I specified mu and got a nice answer.

thanks anyway

> restart; mu := .96;
0.96
> ode := (D(theta))(t) = mu+sin(theta(t));
D(theta)(t) = 0.96 + sin(theta(t))
> dsolve(ode);
/ / 7 \ \
|4 exp|-- t| _C1 - 3 |
| \25 / |
theta(t) = -2 arctan|--------------------|
| /7 \ |
|-4 + 3 exp|-- t| _C1|
\ \25 / /
> ics := theta(0) = 0;
theta(0) = 0
> dsolve({ics, ode});
Is there a better choice for IC?

restart; assume(mu,'real');is(0< mu<1);
ODE:=(ⅆ)/(ⅆt)theta(t)=mu+sin(theta(t));
ans:=dsolve([ODE]);
theta(t):= 2 arctan((tan(1/2 t sqrt(mu^2-1)+1/2 _C1 sqrt(mu^2-1)) sqrt(mu^2-1)-1)/(mu));
ics:=theta(0)=1,D(theta)(0)=0;
dsolve([ODE,ics]);
Gives me the error:
Error, (in dsolve) required an indication of the dependent variables in the given system
What's the problem?

f := proc (r, x) options operator, arrow; r*x+x^3-x^5 end proc;
with(plots)
display([implicitplot(f(r, x), x = -2 .. 2, r = -1 .. -3*x^2+5*x^4, colour = blue, axes = box, gridrefine = 3, crossingrefine = 3), implicitplot(f(r, x), x = -2 .. 2, r = -3*x^2+5*x^4 .. 2, colour = red, axes = box, gridrefine = 3, crossingrefine = 3)]);
display(plottools[rotate](%, 3*Pi*(1/2), [0, 0]), labels = [r, x])
How do I shorten the range in r to -1,2.
I tried adjusting the variables but it still extends beyond r = 2 and I don't want all that garbage.
Do you know how to shorten the range in r?

Also how did you determine the interval for r?

r=cos(x) .. 2

When I try I get Error, (in plots/implicitplot) invalid input: invalid range for first variable

Also how do I switch the axis, X on the vertical and r on the horizontal?

BIFpt2 := [[-4/27, 1/3], [0, 1]];

is useless,

how do I plot the equilibrium points?

After you established your stable points, you are asked to draw the vector fields on the diagram.

I assume r would be the parameter for the animation.

What if I want to plot the vector field for the following function?
f := r*x-sin(x)
I was only able to plot the above with this command:
implicitplot(f = 0, r = -4 .. 4, x = -14 .. 14, style = POINT)
How do I include this in the animate command?