Question

Solve the system.
dx/dt=[-2 -5,] x
[5 -2]
with x(0)=[2, -3].
Give your solution in real form.
x1= ?, x2= ?

Answer 1

What kinda methods are you allowed to use to solve this?

Answer 2

Well, we can use anything apart from diagnolization. However, it wasn't specified in the question what to use to solve this. So any help in this would be appreciated. I've been told it can be solved by the eigen vector and eigenvalue approach.

Answer 3

did you find the eigvals and eigvecs ?

Answer 4

the general sol'n will be
\[ x(t) = c_1 \vec{v_1} e^{\lambda_1 \ t } + c_2 \vec{v_2} e^{\lambda_2 \ t}\]