Hi there.

I am having a little bother plotting a phase portrait of the following system:

DEs := [diff(u(t),t)=-a*u(t)+v(t), diff(v(t),t)=u(t)^2/(1+u(t)^2)-v(t)];

where 'a' denotes any real number.  I am trying to draw the phase portrait but I have know initial conditions. 'a' must also be from -0.5..0.5.

Any hints/tips would be greatly appreciated.  Thanks.

Hi there.

I have two vectors:

x1:= [ ( 1+sqrt(1-4*a^2) )/(2*a) , ( 1+sqrt(1-4*a^2) )/2 ];

x2:= [ ( 1-sqrt(1-4*a^2) )/(2*a) , ( 1-sqrt(1-4*a^2) )/2 ];

I have the following questions to complete:

(2)Determine when x1 and x2 are both real

(3)Determine the largest interval I=(c,d) (with d>0) such that x1 and x2 are real and distinct.

The answers are obvious on paper, but I have to calculate this with Maple.  How do I go about this?

Thanks