Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 341 / 5 / b / 3 / Solution

The Butcher tableau has one stage with $a_{11}=1/2$ and $b_1=1$, so it is the implicit midpoint ruleAgain, interchanging the endpoints and changing $h$ to $-h$ leaves the equation invariant. Hence $\boxed{\text{method 3 is time symmetric}}$.