Add u as an additional variable defined by dh/dt = u
Then enter to Maple in DAE form. My guess is that you are lucky because this approach works for this case as the addition of u enables Maple to convert this system to explicit dy/dt = f form. But in general Maple cannot solve nonlinear DAEs or ODEs if it cannot convert them to explicit ODE form dy/dt = f. In fact, this is a serious flaw. The assumption made here is that all ODEs and DAEs can be converted to dy/dt = f(y) form. This is not true for many nonlinear or implicit ODEs until you add addtional variables. Maple avoids using Newton Raphson or any nonlinear solvers in its ODE solver.
Code attached. It is best to post some range for parameters or the physics of the problem. I can't guess the values of the parameters. You have to find u(0) for every set of parameters. For the parameters I chose, there is a singularity at 3.22 or so.