$\displaystyle \frac{dy}{dx }=\frac{2}{27 }(x-3) \sqrt{\frac{x^2-6x+23}{y } } $

From an earlier part of the question I know that I need to use $\displaystyle f(x)=(x^2 -6x+23)^\frac{3}{2 }$ $\displaystyle f'(x)=\frac{3}{2 }(x^2 -6x+23)^\frac{1}{2 } (2x-6) $

I need a general solution in implicit form and then with y=2 and x=1 an explicit solution