1. The problem statement, all variables and given/known data Solve the following initial value problem using Laplace transforms: y' + 4y = 3t3 e−4t ; y(0) = 0 . Useful information: Recall that the Laplace transform of y 0 is pY − y(0), where Y is the Laplace Transform of y. The Laplace transform of tk e−at is k!/(p + a)k+1 . Confirm the validity of your result by an explicit check. 2. Relevant equations tk e−at is k!/(p + a)k+1 3. The attempt at a solution So I have the solution: y=3/4 t4e−4t And I know this is correct. However is there a specific check I can do to make sure this is correct? ie. What is the explicit check?