Let y(t) = (y1(t), y2(t))^T and A(t) = (a(t) b(t) c(t) d(t)). A(t) is a 2x2 matrix with a,b,c,d all polynomials in t. Consider the two dimensional Cauchy problem y'(t) = A(t)y(t), y(0)=y0. Show that a solution exists for all t>=0. Give a general condition on the A(t) which ensures global existence. Please could you help me with this question - I don't know what to do. I need to use Picard somewhere I think but I don't know how to go about it.