Thread: Need help - difference equation / dynamical system / fixed points

I checked this forum for any potential help with dynamical systems/fixed points. I hope there is anybody who could help me with a couple of homework questions/tasks. I would very much appreciate any help and would also be willing to compensate.

I need to provide solutions for the following questions:

1. To find different forms of the general solution of difference equation y_(t+2)+2y_(t+1)+by_t = 5 ; depending on the value of constant a. To find the fixed points
of dynamical system, defined with this difference equation and to analyze the stability of fixed points for each case. To find for b = 6 the particular solution, if y_0 = 2 and y_1 = 5.

2. To find fixed points of dynamical system x=y^2-4x / y=3y-2x and with the help of linearization to study the local stability of fixed points and to
determine the type of fixed points.

3. To analyze the Phase portrait of the dynamic system x=3y, y=5x-2y
(as in Examples 4.4-4.5 in the Basic textbook of Shone)

I have the related book (R. Shone, Economic Dynamics) as pdf-file available.
I would send the tasks /also attached) and the book to anybody who might be interested to help (and benefit).

Thanks in advance.

Tom