There is no assurance that ever nonlinear differential equatino you may choose to pose has an analytical solution. In fact, I not that just as the symbolic tolbox fails to find a solution, mathematica also seems stumped by it.
Do you have a domein of interest? Do you have known values for the constants? If so, then you can use a numerical solver, like ODE45. That should be fairly simple, as long as you do not pass through a singularity at y==0.
