Overview
The entire homework must be written in Mathematica. Handwritten images will not be accepted. Note, not all parts will require Mathematica functions and can be simply typed using Palettes. All parts should be answered to receive full credit.
only one problem!
following:
Consider 2x2 system
x' = (1 -8
1 -3) x, initial conditions: x(0) = (1
3)
(a) Solve IVP. Clearly show how you computed eigenvalues and eigenvectors by using appropriate Mathematica functions. Express your solution in terms of real-valued functions (10pt)
(b) Plot Direction Field (10pt)
(c) Plot your solution in part (a) as graphs x vs t (10pt)
(d) Plot the corresponding trajectory in the x1x2-plane (10pt)
(e) Classify the critical point (0,0) as to type and its stability (10pt)