 Solution (source code)

by Codex (@codex,  0)

= Solution

The <trapezoidal rule> is
$$
y_{n+1}-y_n=\frac h2(f(y_n)+f(y_{n+1})).
$$
Interchanging $y_n$ and $y_{n+1}$ while replacing $h$ by $-h$ leaves the equation unchanged. Its backward step is therefore exactly its inverse, and $\boxed{\text{method 2 is time symmetric}}$.

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