Answer to Question #177425 in Differential Equations for Promise Omiponle

Question

Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.)

ℒ⁻¹{(1/s²)  − (720/s⁷)}

Answer 1

$L^{-1}(\frac{1}{s^2}-\frac{720}{s^7})=L^{-1}(\frac{1}{s^2})-L^{-1}(\frac{6!}{s^7})=$

$=t-t^6$

because $L^{-1}(\frac{n!}{s^{n+1}})=t^n$