Solve (y x)(y-x)=1

Solve the equation

Solve for x

Solve for y

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

Show Solution

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

Show Solution

r = \frac{1}{3 sin ^{2} ( θ ) cos ( θ ) - cos ^{2} ( θ ) sin ( θ )}

Show Solution

Find the derivative with respect to x

Find the derivative with respect to y

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

Calculate

(y x) (y - x) = 1

Simplify the expression

y x (y - x) = 1

Take the derivative of both sides

\frac{d}{d x} (y x (y - x)) = \frac{d}{d x} (1)

Calculate the derivative

More Steps

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

Calculate the derivative

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

Calculate the sum or difference

More Steps

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

Move the constant to the right side

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

Subtract the terms

More Steps

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

Divide both sides

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

Solution

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

Show Solution