DSolve[Derivative[1][y][x] == (6*y[x])/(-F[x - y[x] - y[x]^2 - y[x]^3/2 - y[x]^4/3] + 6*y[x] + 12*y[x]^2 + 9*y[x]^3 + 8*y[x]^4),y[x],x]