- Just because you want it to happen, symbolic solutions need not always exist for all problems. In fact, it is a vanishingly small number of problems with symbolic solutions.
- You can always use a numerical solver, perhaps ODE45 might be a good place to start. It will probably fail, because at y(1/2) == 1/2, there is a derivative singularity.
- Finally, sometimes a solution can be found by a clever transformation of the problem. This is why they pay the mathematicians the big bucks. (Yeah, right. Like that often happens.) Ok, the good mathematicians.
- The derivative singularity at y(1/2) == 1/2 may suggest a good transformation may exist, but you would need to be creative.
Ok, do you want something a bit more useful? If I had to guess, no explicit solution probably exists. The result is going to exist, if at all, as an implicit function.
