That's what I said. The Mathieu equation is not exactly the same as a variable capacitance resonant equation but it is close.

say that C(t)=C0*(1+a cos(t)). Dividing through by (1+a cos(t)) is close to multiplying by (1-a cos(t)) for small a. And there you have the Mathieu equation, apart from the C' * V' term. That cross-term does not show up in the derivations for sloshing dynamics in any of the papers and books that I have read on the subject. Faltinsen[1] adds a first-order damping term which may override that factor.

[1]O. M. Faltinsen and A. N. Timokha, Sloshing. Cambridge University Press, 2009.