1. (a) f = a0(t)y + a1(t)y + a2(t)y + + an(t)y(n) + g(t), (b) (i) second order and linear; (ii) third order and non-linear; (iii) rst order and linear. an(t) 6= 0. 2. (a) y(t) = e t e 2t. (b) all real numbers; all values of would make the limit 0. (c) = 0 only. 3. (a) y = 0 and y = 3. (b) y = 0 is a stable equilibrium solution, y = 3 is an unstable equilibrium solution. (c) since y = 0 is an equilibrium solution, it"s a constant solution. Therefore, if y(0) = 0 then y(1) = 0. [ 3t cos t + 3 sin t 3] = 3t cot t + 3 3 csc t. (b) (0, ) is the largest interval. = c, or (after rst dividing both sides by x y), y = x + c: (a) q = .
