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

Integrating term by term, we have:

\(y = \int (3x^2) \, dx - \int \left(\frac{2}{x^3}\right) \, dx\)

\(y = \frac{3x^3}{3} - \frac{2x^{-2}}{-2} + c\)

\(y = x^3 + x^{-2} + c\)

Since the curve passes through \((-1, 3)\), substitute \(x = -1\) and \(y = 3\) to find \(c\):

\(3 = (-1)^3 + (-1)^{-2} + c\)

\(3 = -1 + 1 + c\)

\(3 = c\)

Thus, the equation of the curve is \(y = x^3 + x^{-2} + 3\).