x1(t) and x2(t) are functions of t which are solutions of the system of differential equations
x(dot)1 = 4x1 + 3x2
x(dot)2 = -6x1 - 5x2
Express x1(t) and x2(t) in terms of the exponential function, given that x1(0) = 1 and x2(0) = 0
The Attempt at a Solution
I've already put this into matrix form,
To find that the eigenvalues are -2 and 1, and then that the eigenvectors are
but after that I'm completely stuck. I know you get into constants and such but I just can't remember how to continue.