Solve x^{2017} - 1 = (x - 1)(y^{2015} - 1)

Calculate

x^{2017} - 1 = (x - 1) (y^{2015} - 1)

Take the derivative of both sides

\frac{d}{d x} (x^{2017} - 1) = \frac{d}{d x} ((x - 1) (y^{2015} - 1))

Calculate the derivative

More Steps

2017 x^{2016} = \frac{d}{d x} ((x - 1) (y^{2015} - 1))

Calculate the derivative

More Steps

2017 x^{2016} = y^{2015} - 1 + 2015 x y^{2014} \frac{d y}{d x} - 2015 y^{2014} \frac{d y}{d x}

Swap the sides of the equation

y^{2015} - 1 + 2015 x y^{2014} \frac{d y}{d x} - 2015 y^{2014} \frac{d y}{d x} = 2017 x^{2016}

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

y^{2015} - 1 + (2015 x y^{2014} - 2015 y^{2014}) \frac{d y}{d x} = 2017 x^{2016}

Move the constant to the right side

(2015 x y^{2014} - 2015 y^{2014}) \frac{d y}{d x} = 2017 x^{2016} - (y^{2015} - 1)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

(2015 x y^{2014} - 2015 y^{2014}) \frac{d y}{d x} = 2017 x^{2016} - y^{2015} + 1

Divide both sides

\frac{( 2015 x y ^{2014} - 2015 y ^{2014} ) \frac{d y}{d x}}{2015 x y ^{2014} - 2015 y ^{2014}} = \frac{2017 x ^{2016} - y ^{2015} + 1}{2015 x y ^{2014} - 2015 y ^{2014}}

Solution

\frac{d y}{d x} = \frac{2017 x ^{2016} - y ^{2015} + 1}{2015 x y ^{2014} - 2015 y ^{2014}}

Solve the equation

Testing for symmetry

Find the first derivative