Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 36A / b / Solution

For $R(s)=|x-y(s)|$ and $|v|<c$, the function $F(s)=s+R(s)/c$ has
$$
F'(s)=1-\widehat R\cdot v/c>0.
$$
It is strictly increasing, so the retarded-time equation has at most one solution.

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