What is implicit x^3y^2=xy^3+6 ?

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

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implicit x^3y^2=xy^3+6

implicit derivative

x^{3} y^{2} = x y^{3} + 6

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

Solution steps

x^{3} y^{2} = x y^{3} + 6

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{y ( y - 3 x ^{2} )}{x ( 2 x ^{2} - 3 y )}

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

\int \frac{1}{x ^{2} x ^{2} - 15} d x

y = x^{2}, y = - x + 2

\frac{1}{( s - 1 ) ^{3}}

\int (9 x e^{x^{2}} + \frac{5}{x} - 5^{x} + 3 x^{2}) d x

x \to - 2 lim (n (x))

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