Solution
= Solution
The <Taylor expansions> about $t_n$ are
$$
y_{n\pm1}=y_n\pm hy'_n+\frac{h^2}{2}y''_n\pm\frac{h^3}{6}y'''_n+\frac{h^4}{24}y^{(4)}_n+O(h^5).
$$
Adding them cancels the <odd>[odd] powers of $h$ and gives
$$
\frac{y_{n+1}-2y_n+y_{n-1}}{h^2}
=y''(t_n)+\frac{h^2}{12}y^{(4)}(t_n)+O(h^4).
$$
Thus the <centred finite difference> has <truncation error> $O(h^2)$, so $\boxed{\alpha=2}$.