1. (+ 20) For each of the following equations determine whether the equation is autonomous (A), lin- ear homogeneous (LH), linear inhomogeneous (LI), nonlinear (N) or separable (S). Please clearly indicate your response by circling the appropriate answer. Some equations may fit multiple cate- gories or none of the categories. A (autonomous) LH (homog) LI (inhomog) N (nonlinear) S (separable) dy (a) dx A LH LI N S dy (b) dx = 3xy A LH LI N S (C) dx dy = 2y(1 - y) A LH LI N S dy (d) x- dx = xy - sin(x) A LH LI N S dy 1 (e) dx = 2 A LH LI N S xy 2. (+ 10) Is y(x) = e2 a solution to the differential equation y" - -y' - 16xy = 0? Justify your answer with a calculation