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Answers for “如何验证隐式解是正确的?”

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The final implicit solution for the example equation (-3x^2 - y)dx+(3y2−x)dy=0dx + (3y^2 - x)dy = 0 is -x^3+y33 + y^3 - xy = C.

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

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The presenter leaves the answer in implicit form because the equation contains multiple powers and products of y, making it cumbersome to solve explicitly for y.

Conditions: The solution contains multiple y terms.; An explicit solution for y is not attempted.