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We show that the solutions to the second-order differential equationassociated to the generalised Chazy equation with parameters $k=2$ and $k=3$naturally show up in the conformal rescaling that takes a representative metricin Nurowski's conformal class associated to a maximally symmetric$(2,3,5)$-distribution (described locally by a certain function$\varphi(x,q)=\frac{q^2}{H''(x)}$) to a Ricci-flat one.

Nurowski's conformal class of a maximally symmetric (2,3,5)-distribution and its Ricci-flat representatives