The ability of Maple to solve differential equations is unsurpassed, but when the solutions appear in terms of Heun functions that result is disappointing because it is either difficult or impossible to convert those functions to other functions more commonly used and for which plots are readily generated.
Specifically, does any reader have a suggestion what to do with Heun C and Heun G functions? In principle, they seem to be related to 1F1 and 2F1 hypergeometric functions, but the conversion seems not to succeed, and it is not obvious how to make it succeed. In both cases of interest, the literature contains hints of solutions in other functions.
It seems that a solution of a differential equation in terms of Heun functions is not a solution at all.