To solve this problem, we'll start by integrating the given derivative \(\frac{dy}{dx}\) to find the original function \(y(x)\).

Given: \(\frac{dy}{dx} = 2x - 3\).

Integrating both sides with respect to \(x\):

\int \frac{dy}{dx} dx = \int (2x - 3) dx\)

y = x^2 - 3x + C\),

where \(C\) is the constant of integration.

Now, we'll use the initial condition \(y = 3\) when \(x = 0\) to find the value of \(C\):

3 = (0)^2 - 3(0) + C\)

C = 3\).

Therefore, the equation of the function \(y(x)\) is:

y(x) = x^2 - 3x + 3\).