Consider a system of differential equations which has the general solution: = C1 e-5-t + C2 -1 (a) Determine the fundamental matrix O (t) which has the property (0) = I. 15 2t 8 -5t 15 -5t 8 (t) = 1...

Extracted text: Consider a system of differential equations which has the general solution: = C1 e-5-t + C2 -1 (a) Determine the fundamental matrix O (t) which has the property (0) = I. 15 2t 8 -5t 15 -5t 8 (t) = 1 12t -5t е + 8 (b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions: a (t) = 3e-5t y (t) = 2t ;8]-[? x (0) (ii) x (t) = y (t) =