When b2 show that the differential equation in the above

Question

Consider

, if A(t) is a fundamental matrix with A(0)= I and p(t) has period k

1) Show that det A(t)= 1 for all t then use this to show that the floquet multipliers are roots of x²-bx+1=0 when b is the trace of A(k)

2) When b=2 show that the differential equation in the above figure has a solution of period k.