To find the equation of the curve, we need to integrate \(\frac{dy}{dx} = x^3 - \frac{4}{x^2}\).

Integrating term by term, we have:

\(\int x^3 \, dx = \frac{x^4}{4}\)

\(\int -\frac{4}{x^2} \, dx = \int -4x^{-2} \, dx = 4x^{-1} = \frac{4}{x}\)

Thus, the general solution is:

\(y = \frac{x^4}{4} + \frac{4}{x} + C\)

We use the point \(P(2, 9)\) to find \(C\):

Substitute \(x = 2\) and \(y = 9\) into the equation:

\(9 = \frac{2^4}{4} + \frac{4}{2} + C\)

\(9 = 4 + 2 + C\)

\(9 = 6 + C\)

\(C = 3\)

Therefore, the equation of the curve is:

\(y = \frac{x^4}{4} + \frac{4}{x} + 3\)