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We discuss symmetries of Hamiltonians of I$_{38}$ and I$_{49}$ equations thatappear on Ince's list of fifty second-order differential equations withPainlev\'e property. This study is informed by structure of Weyl symmetries ofPainlev\'e P$_{III}$ and mixed Painlev\'e P$_{III-V}$ equations and providesinsights into differences between the symmetries of Painlev\'e equations andsymmetries of solvable equations on Ince's list.

Symmetries and hamiltonians of Ince's XXXVIII and XLIX equations