Solve x^2y^2 - 9x^2 - 4y^2 = 0

Question

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Symmetry with respect to the origin

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Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{- x y ^{2} + 9 x}{x ^{2} y - 4 y}

Calculate

x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0

Take the derivative of both sides

\frac{d}{d x} (x^{2} y^{2} - 9 x^{2} - 4 y^{2}) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

2 x y^{2} + 2 x^{2} y \frac{d y}{d x} - 18 x - 8 y \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

2 x y^{2} + 2 x^{2} y \frac{d y}{d x} - 18 x - 8 y \frac{d y}{d x} = 0

Collect like terms by calculating the sum or difference of their coefficients

2 x y^{2} - 18 x + (2 x^{2} y - 8 y) \frac{d y}{d x} = 0

Move the constant to the right side

(2 x^{2} y - 8 y) \frac{d y}{d x} = 0 - (2 x y^{2} - 18 x)

Subtract the terms

More Steps

(2 x^{2} y - 8 y) \frac{d y}{d x} = - 2 x y^{2} + 18 x

Divide both sides

\frac{( 2 x ^{2} y - 8 y ) \frac{d y}{d x}}{2 x ^{2} y - 8 y} = \frac{- 2 x y ^{2} + 18 x}{2 x ^{2} y - 8 y}

Divide the numbers

\frac{d y}{d x} = \frac{- 2 x y ^{2} + 18 x}{2 x ^{2} y - 8 y}

Solution

More Steps

\frac{d y}{d x} = \frac{- x y ^{2} + 9 x}{x ^{2} y - 4 y}

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