X(y^2-1)dx-y(x^2-1)dy=0

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Solution for X(y^2-1)dx-y(x^2-1)dy=0 equation: 


Simplifying
X(y2 + -1) * dx + -1y(x2 + -1) * dy = 0

Reorder the terms:
X(-1 + y2) * dx + -1y(x2 + -1) * dy = 0

Reorder the terms for easier multiplication:
X * dx(-1 + y2) + -1y(x2 + -1) * dy = 0

Multiply X * dx
dxX(-1 + y2) + -1y(x2 + -1) * dy = 0
(-1 * dxX + y2 * dxX) + -1y(x2 + -1) * dy = 0
(-1dxX + dxy2X) + -1y(x2 + -1) * dy = 0

Reorder the terms:
-1dxX + dxy2X + -1y(-1 + x2) * dy = 0

Reorder the terms for easier multiplication:
-1dxX + dxy2X + -1y * dy(-1 + x2) = 0

Multiply y * dy
-1dxX + dxy2X + -1dy2(-1 + x2) = 0
-1dxX + dxy2X + (-1 * -1dy2 + x2 * -1dy2) = 0

Reorder the terms:
-1dxX + dxy2X + (-1dx2y2 + 1dy2) = 0
-1dxX + dxy2X + (-1dx2y2 + 1dy2) = 0

Solving
-1dxX + dxy2X + -1dx2y2 + 1dy2 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1xX + xy2X + -1x2y2 + y2) = 0


Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
d = 0

Subproblem 2
Set the factor '(-1xX + xy2X + -1x2y2 + y2)' equal to zero and attempt to solve:

Simplifying
-1xX + xy2X + -1x2y2 + y2 = 0

Solving
-1xX + xy2X + -1x2y2 + y2 = 0

Move all terms containing d to the left, all other terms to the right.

Add 'xX' to each side of the equation.
-1xX + xy2X + -1x2y2 + xX + y2 = 0 + xX

Reorder the terms:
-1xX + xX + xy2X + -1x2y2 + y2 = 0 + xX

Combine like terms: -1xX + xX = 0
0 + xy2X + -1x2y2 + y2 = 0 + xX
xy2X + -1x2y2 + y2 = 0 + xX
Remove the zero:
xy2X + -1x2y2 + y2 = xX

Add '-1xy2X' to each side of the equation.
xy2X + -1x2y2 + -1xy2X + y2 = xX + -1xy2X

Reorder the terms:
xy2X + -1xy2X + -1x2y2 + y2 = xX + -1xy2X

Combine like terms: xy2X + -1xy2X = 0
0 + -1x2y2 + y2 = xX + -1xy2X
-1x2y2 + y2 = xX + -1xy2X

Add 'x2y2' to each side of the equation.
-1x2y2 + x2y2 + y2 = xX + -1xy2X + x2y2

Combine like terms: -1x2y2 + x2y2 = 0
0 + y2 = xX + -1xy2X + x2y2
y2 = xX + -1xy2X + x2y2

Add '-1y2' to each side of the equation.
y2 + -1y2 = xX + -1xy2X + x2y2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = xX + -1xy2X + x2y2 + -1y2

Simplifying
0 = xX + -1xy2X + x2y2 + -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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