Question

Find the matrix A and vector b if the given system is written as x' = Ax + b

x'1 = (e^t)*x1 - (e^-t)*x2 + cos(5t)
x'2 = 2*(e^-t)*x1 + 3*(e^t)*x2 - 2*sin(5t)

Answer 1

A = [e^t -e^-t]
[2e^-t 3e^t]

b = [ cos(5t) ]
[-2sin(5t)]