What is implicit x^3+y^3=18xy ?

The answer to implicit x^3+y^3=18xy is (dy)/(dx)=(6y-x^2)/(y^2-6x)

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implicit x^3+y^3=18xy

implicit derivative

x^{3} + y^{3} = 18 x y

\frac{d y}{d x} = \frac{6 y - x ^{2}}{y ^{2} - 6 x}

Solution steps

x^{3} + y^{3} = 18 x y

Treat

y

y (x)

Differentiate both sides:

3 x^{2} + 3 y^{2} \frac{d y}{d x} = 18 (y + x \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{6 y - x ^{2}}{y ^{2} - 6 x}

\frac{d y}{d x} = \frac{6 y - x ^{2}}{y ^{2} - 6 x}

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\int_{0}^{1} \frac{58}{4 y - 1} d y

\frac{d y}{d x} = \frac{x y}{2}

\int \frac{2 x ^{3} + 11 x + 8}{x ^{3} + 4 x ^{2} + 4 x} d x

What is implicit x^3+y^3=18xy ?
The answer to implicit x^3+y^3=18xy is (dy)/(dx)=(6y-x^2)/(y^2-6x)