Solve the IVP $$\frac{d^2y}{dt^2}+12\frac{dy}{dt}+72 y=0, y(0) = 0, y^\prime(0)=-6$$
The Laplace transform of the solutions is L{y} =
By completing the square in the denominator we see that this is the Laplace transform of shifted by the rule (Your first answer blank for this question should be a function of t).
Therefore the solution is y =