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\includegraphics[max width=\textwidth, alt={}, center]{3621a7e5-a3fb-42c1-828d-7068fddbf2f9-3_677_691_781_724} A particular solution of the differential equation $$3 y ^ { 2 } \frac { \mathrm {~d} y } { \mathrm {~d} x } = 4 \left( y ^ { 3 } + 1 \right) \cos ^ { 2 } x$$ is such that \(y = 2\) when \(x = 0\). The diagram shows a sketch of the graph of this solution for \(0 \leqslant x \leqslant 2 \pi\); the graph has stationary points at \(A\) and \(B\). Find the \(y\)-coordinates of \(A\) and \(B\), giving each coordinate correct to 1 decimal place.