Wow, great reply Doug, thank you. I have tried the following to no avail however :(

>opts := stepsize=0.1, method=classical[rk4], thickness=1, 
colour=red, linecolour=blue, scene=[u,v]:

> T:=10:

> DEplot( [seq(eval(op(DEs),a=k),k=-0.5..0.5,0.1)],vars(t), 
t=-T..T, u=-.3..0.3, v=-.3..0.3 ,opts);

No initial conditions were needed if I tried a single value for a. But when trying to produce a portrait over the whole range, I receive "Error, (in DEtools/DEplot/InputCheck) System must have same number of dependent variables as DE's." I'm guessing this is because each value for a will produce it's own portrait, hence trying to plot one over a range is unacceptable. Is this correct? Will I have to create many, then use 'display'? The question says "plot the phase portrait of the differential equations for values of a in the relevant intervals". Thanks.

where 'know'=no above.  Editing posts should be allowed.

Thank you Doug.  The project itself is exploring the Saddle-Node Bifurcation, which essentially entails obtaining the equilibria of a system of differential equations, producing the linearization and plotting a phase portrait (amongst other things).

>There is no pre-packaged Maple command that I know for directly answering your >questions.

Yes this is why I was stumped, a simple 'solve()' just didn't enter my mind.

Thanks for your help, Doug.

Sorry I realise giving answers is not acceptable, but I am just a bit stumped by this one.  I am fairly familiar with Maple, I just couldn't, for the life of me, find a suitable answer.

While solve(1-4*a^2>=0,a); produces the solution, it implies I know something about the vectors, as I have just picked the relevant part to calculate an answer.  This doesn't sit right with me, although it may well be what they're looking for.

 

Thanks for the reply.

Thats is precisely what I was asking though, I don't know how to obtain an answer for it.  The help menu doesn't help as I don't know what to search for.

Well clearly 'a' must be in the interval [-1/2,1/2] (inclusive) for x1 and x2 to be real.

And for them to be distinct, 'a' must be in the interval (-1/2,1/2) (not inclusive).

Correct?

 

Anyway, I'm pretty sure I must calculate this somehow as it details at the bottom of the project sheet "The computations in all steps must be done in Maple".

 

Thanks