Question

Problem #4: Find the inverse Laplace transform of the following expression 10s 3 2-251 Enter your answer as a symbolic function of t, as in these examples Problem #4 Submit Problem #4 for Grading Just Save Attempt #4 Attempt #5 Attempt #3 Problem #4 Attempt #2 Attempt #1 Your Answer: Your Mark:

Answer 1

Require to evaluate the inverse Laplace transform of the given expression: 10s + 3/s^2 - 2s + 1 Using partial fraction decomposition, we have 10s + 3/s^2 - 2s + 1 = A/s - 1 + B/(s - 1)^2 10s + 3/s^2 - 2s + 1 = A (s - 1) + B/(s - 1)^2 10s + 3 = A (s - 1) + B Now equating coefficients of s: 10 = A - A + B = 3 Implies - 10 + B = 3 Implies B = 13 Using the above, we have 10s + 3/s^2 - 2s + 1 = 10/s - 1 + 13/(s - 1)^2 Now the inverse transform of the given expression is L^-1 {10s + 3/s^2 - 2s + 1} = 10 L^-1 {1/s - 1} + 13 L^-1 {1!/(s - 1)^1 + 1} = 10e^t + 13e^t t (L^-1 {1/s - a} = e^at and L^-1 {n!/(s - a)^1 + 1} = e^at t^n) Therefore, L^-1 {10s + 3/s^2 - 2s + 1) = (10 + 13t) e^t