Solution 3.

Exercise 1(a)  Find the general solution to the system of D. E.'s  

First, set up the system of D. E. to be solved.

Find the eigenvalues and eigenvectors of the matrix A and use them to form the vector function solutions to the system of D. E.'s.

The fundamental matrix is F[t] = [X1[t], X2[t]]

Exercise 1(b)  Find the solution with the initial conditions:

We can plot the solution curve.  This is just for fun.

Aside. We will plot the solution curves where the starting points are (1,0), (0,1), (0.5,1), (1,0.5),
and the parameter t is in the interval    This is just for fun!

Plot the solution curves where the starting points are (1,0), (0,1), (0.5,1), (1,0.5).