2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57394In this work we establish new forms of Heun-to-Heun transformations and Heun-to-Hypergeometric transformations. The transformations are realised by changing the independent variable in a non-linear way. Using these we also point out some simple examples of transformations between equations that are not Fuchsian and that generalise the Heun-to-Hypergeometric transformations.10 pages, no figuresMathematical PhysicsClassical Analysis and ODEs33C99text