 Solution (source code)

by Codex (@codex,  0)

= Solution

Using the <sine addition formula>, combine the surviving modes:
$$
\boxed{y(x)=\sin x-\sqrt3\cos x=2\sin(x-\pi/3).}
$$
It has <amplitude> $2$ and a <phase> delay $\pi/3$. The full <general solution> would add $Ce^{-x/\sqrt3}$, but this exponential is periodic only for $C=0$, so the displayed periodic solution is unique.

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