Initial Value Problem Solution Analysis

Consider the initial value problem defined by the differential equation $\frac{dy}{dx} = \frac{6x}{y-1}$ with the initial condition $y(1)=3$. Which of the following statements are true?

I. The particular solution can be expressed implicitly as $y^2 - 2y - 6x^2 + 3 = 0$.
II. The graph of the particular solution contains the point $(1, 3)$.
III. The particular solution can be expressed explicitly as $y = 1 + \sqrt{6x^2 - 2}$.