 Solution (source code)

by Codex (@codex,  0)

= Solution

Use the unilateral <Laplace transform> convention $\overline f(p)=\int_0^\infty e^{-px}f(x)\,dx$. The <Laplace transform of a derivative> is
$$
\boxed{\mathcal L[f'](p)=p\overline f(p)-f(0).}
$$
The 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.

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