Solve 3x^2-2x y^3x-2=y

Question

Solve the equation

x = \frac{3 y - 2 y ^{4} + 6 - 4 y ^{3}}{∣ 3 - 2 y ^{3} ∣} x = - \frac{3 y - 2 y ^{4} + 6 - 4 y ^{3}}{∣ 3 - 2 y ^{3} ∣}

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not 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{6 x - 4 x y ^{3}}{6 x ^{2} y ^{2} + 1}

Calculate

3 x^{2} - 2 x y^{3} x - 2 = y

Simplify the expression

3 x^{2} - 2 x^{2} y^{3} - 2 = y

Take the derivative of both sides

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

Calculate the derivative

More Steps

6 x - 4 x y^{3} - 6 x^{2} y^{2} \frac{d y}{d x} = \frac{d}{d x} (y)

Calculate the derivative

More Steps

6 x - 4 x y^{3} - 6 x^{2} y^{2} \frac{d y}{d x} = \frac{d y}{d x}

Move the variable to the left side

6 x - 4 x y^{3} - 6 x^{2} y^{2} \frac{d y}{d x} - \frac{d y}{d x} = 0

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

6 x - 4 x y^{3} + (- 6 x^{2} y^{2} - 1) \frac{d y}{d x} = 0

Move the constant to the right side

(- 6 x^{2} y^{2} - 1) \frac{d y}{d x} = 0 - (6 x - 4 x y^{3})

Subtract the terms

More Steps

(- 6 x^{2} y^{2} - 1) \frac{d y}{d x} = - 6 x + 4 x y^{3}

Divide both sides

\frac{( - 6 x ^{2} y ^{2} - 1 ) \frac{d y}{d x}}{- 6 x ^{2} y ^{2} - 1} = \frac{- 6 x + 4 x y ^{3}}{- 6 x ^{2} y ^{2} - 1}

Divide the numbers

\frac{d y}{d x} = \frac{- 6 x + 4 x y ^{3}}{- 6 x ^{2} y ^{2} - 1}

Solution

More Steps

\frac{d y}{d x} = \frac{6 x - 4 x y ^{3}}{6 x ^{2} y ^{2} + 1}

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