Follow-up Comment #1, bug #581 (project tex4ht):
I would say that this is an issue in MathJax. As I already said in my answer
on TeX.sx, it seems to interpret the square brackets after start of the
aligned environment as an optional parameter, so it discards it. Use this
instead:
\begin{aligned}
\left[y \left(0\right) = 3\right]
\end{aligned}
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