APPM 2360 Midterm: archive_appm2360fall2018exam3_sol
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Problem 1 (true/false) are the following statements true or false? (only answer true or. If a statement is not always true, reply false". Give your answers in the bluebook (and not on this problem sheet). (a) observe that y(t) = cos(2t) is a solution to the ode y y + 4y = 2 sin(2t). Solution: (a) false (b) false (c) true (d) true (e) false (f) true (g) false (h) true (i) false (j) true. Problem 2 the following questions are unrelated. (a) find a particular solution to using the method of undetermined coe cients. y 4y 12y = 4e3t (b) find the full general solution to y + 4y = Hint: r tan(at)dt = 1 a ln (cos(at)) + c. Solution: (a) first we guess yp(t) = ae3t. 15 e3t . y h + 4yh = 0 with characteristic equation r2 + 4 = 0 giving r = 2i. Thus, yh(t) = c1 cos(2t) + c2 sin(2t)
