Past exam of the short options course of the University of Oxford / 2015 / 5 / a / i / Solution

Use the unilateral Laplace transform convention $\overline{f}(p)={\int }_0^{\infty }{e}^{-px}f(x)dx$. The Laplace transform of a derivative isThe formula holds in the common Laplace convergence region under the usual endpoint and growth hypotheses. The initial value is the right-hand value at zero.