Final answer:
The provided general solution cannot be obtained from the given differential equation without additional context or steps. More information is needed to solve the problem or verify the solution.
Step-by-step explanation:
The given differential equation dy/dx = 6xy² - 6x + 3y² - 3 cannot be solved directly as presented in the question, because it appears to lack a clear direction for separation of variables or integration. The provided general solution y - 1/y + 1 = Ce⁶x² + 6x cannot be obtained from the given differential equation without additional context or steps. Therefore, to give a precise answer, we need either a correct differential equation that matches the general solution provided or further information on how to derive the general solution from the given differential equation. Without this information, we cannot confidently proceed with solving the problem or confirming the proposed solution.