Question

Previous Problem Problem List Next Problem (1 point) Use the Laplace transform to solve the following initial value problem: y" - y' – 12y = 0, y(0) = -7, y'(0) = 7 (1) First, using Y for the Laplace transform of y(t), l.e., Y = L(y(t)) find the equation you get by taking the Laplace transform of the differential equation to obtain =0 (2) Next solve for Y = A B (3) Now write the above answer in its partial fraction form, Y = = Y= 3-at 3 - 6 (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1) Y = (4) Finally apply the inverse Laplace transform to find y(t) g(t) =

Answer 1

y" - y - 12y=o. Gos=-7 y cost (Y") - Lly) 12414)=0 8²4 (8) -4(0)- 8410) - 848) +40-12418)= 0 (82-8-12) 418) +7-78-4 = 0 (8²-8-12)418) = 78 Y(s) - 78 - (8+3)(8+4) (4 (8) = 8.4 - 3+3] YH = (t)- I' l 3272) [y(t) = 8 _ (34] #