Show all your work in the space provided under each question. Please write neatly and present your answers in an organized way: solve the initial value problem x + 4x = (t 2) x(0) = 1 x (0) = 0. 4(cid:1) as the product of a number and (cid:0) 1. Page 2 (b) given that (cid:0) 1. 2(cid:1) = , nd (cid:0) 3. 2(cid:1) : find the general solution to the system: = 3x y: solve using the laplace transforms. Of course, it is possible to solve this using other methods, but you will receive credit only if you use laplace transform methods. x + 2x + 5x = e3t x(0) = x (0) = 0. Page 4: use the euler method with stepsize . 5 to estimate x(1) and y(1) for the initial. = 2x y y(0) = 0: solve x x 2x = (t) x(0) = 1 x (0) = 0.
