Question

Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y Find Y(s), the Laplace transform ofy() Enter your answer as a symbolic function of s, as in these examples Problem #2: Submit Problem #2 for Grading Just Save Attempt #3 Problem #2 Attempt # 2 Attempt #5 Attempt#1 Attempt #4 Your Answer: Your Mark

Answer 1

"Consider diff. eqn. y"" + zy = e^st, y(0) = 6, y'(0) = 3 Taking L.T. on both sides L {y""} + 7 L {y} = L {e^st} S^2 L {y} - Sy(0) - y'(0) + 7L{y} = 1/s - 8 (s^2 + 7) L{y} - 6S - 3 = 1/s - 8 y(s) = L {y} = 6S + 3/S^2 + 7 + 1/(S - 8) (s^2 + 7) * Now taking L^-1 y(t) = L^-1 {6S + 3/S^2 + 7} + L^-1 {1/(S - 8) (S^2 + 7)} = 6 cos squareroot 7 t + 3/squareroot 7 sin squareroot 7 t + L^-1 {1/(S - 8) (S^2 + 7)} ** Let 1/(S - 8) (S^2 + 7) = A/S - 8 + BS + /S^2 + 7 1 = A (S^2 + 7) + (BS + C) (S - 8) 1 = S^2 (A + B) + S (-8B + C) + 7A"