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The final implicit solution for the example equation (-3x^2 - y)$dx + (3y^2 - x)dy = 0$ is -x^$3 + y^3$ - xy = C.

Conditions: The equation is exact.; The terms are combined correctly without double-counting.

The final implicit solution for the example equation (-3x^2 - y)$dx + (3y^2 - x)dy = 0$ is -x^$3 + y^3$ - xy = C.

Conditions: The equation is exact.; The terms are combined correctly without double-counting.

The steps involve finding the potential function $F(x,y)$ by integrating M with respect to x and N with respect to y, then combining the results to form the implicit solution $F(x,y) = C$.

Conditions: The differential equation has been verified as exact.

The steps involve finding the potential function $F(x,y)$ by integrating M with respect to x and N with respect to y, then combining the results to form the implicit solution $F(x,y) = C$.

Conditions: The differential equation has been verified as exact.