1. Recall the E\&U Theorem for linear homogeneous ODEs. (a) Let -6, if t <0 p(t) = { -5, if t>09(t) = { 9, if t <0 6, if t> 0 Find the general solution for the equation on y+p(t)y + q(t)y = 0 tB 0 . What is the dimension of the solution space? Why it doesn't contradict the uniqueness of solutions for second order linear equations? (b) Let be a A(t) 3 x 3 matrix of coefficients continuous on and (1,2) (4,5) . Consider the linear ODE x = A(t)x What is the dimension of solutions on