Let y1t and y2t be two linearly independent solutions of y

Question

Show that if y(t) is a solution of y'' + a(t)y = 0, then so is y(t+w), let y₁(t) and y₂(t) be two linearly independent solutions of y'' +a(t)y = 0 satisfying normalized initial conditions y₁(0)=1, y₁'(0)=0 ,y₂(0)=0 , y₂'(0)=1 show that the multipliers satisfy r² - (y₁(w)+y₂'(w) )r + 1= 0.