Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 356 / 1 / d / Solution

The backward equations for the two mean hitting times arewith ${\tau }^{-}(0)=0$ and ${\tau }^{+}(L)={\tau }^{-}(L)$. Their difference obeysand the reflecting condition fixes ${\tau }^{+}-{\tau }^{-}=2(L-y)/s$. Integration then givesand