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

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


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

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

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

Multiply x * dx
dx2(-1 + y) + (x2 + -1) * dy = 0
(-1 * dx2 + y * dx2) + (x2 + -1) * dy = 0
(-1dx2 + dx2y) + (x2 + -1) * dy = 0

Reorder the terms:
-1dx2 + dx2y + (-1 + x2) * dy = 0

Reorder the terms for easier multiplication:
-1dx2 + dx2y + dy(-1 + x2) = 0
-1dx2 + dx2y + (-1 * dy + x2 * dy) = 0

Reorder the terms:
-1dx2 + dx2y + (dx2y + -1dy) = 0
-1dx2 + dx2y + (dx2y + -1dy) = 0

Combine like terms: dx2y + dx2y = 2dx2y
-1dx2 + 2dx2y + -1dy = 0

Solving
-1dx2 + 2dx2y + -1dy = 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(-1x2 + 2x2y + -1y) = 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 '(-1x2 + 2x2y + -1y)' equal to zero and attempt to solve:

Simplifying
-1x2 + 2x2y + -1y = 0

Solving
-1x2 + 2x2y + -1y = 0

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

Add 'x2' to each side of the equation.
-1x2 + 2x2y + x2 + -1y = 0 + x2

Reorder the terms:
-1x2 + x2 + 2x2y + -1y = 0 + x2

Combine like terms: -1x2 + x2 = 0
0 + 2x2y + -1y = 0 + x2
2x2y + -1y = 0 + x2
Remove the zero:
2x2y + -1y = x2

Add '-2x2y' to each side of the equation.
2x2y + -2x2y + -1y = x2 + -2x2y

Combine like terms: 2x2y + -2x2y = 0
0 + -1y = x2 + -2x2y
-1y = x2 + -2x2y

Add 'y' to each side of the equation.
-1y + y = x2 + -2x2y + y

Combine like terms: -1y + y = 0
0 = x2 + -2x2y + y

Simplifying
0 = x2 + -2x2y + y

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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