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

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


Simplifying
X2(y + -1) * dx + y2(x + -1) * dy = 0

Reorder the terms:
X2(-1 + y) * dx + y2(x + -1) * dy = 0

Reorder the terms for easier multiplication:
X2 * dx(-1 + y) + y2(x + -1) * dy = 0

Multiply X2 * dx
dxX2(-1 + y) + y2(x + -1) * dy = 0
(-1 * dxX2 + y * dxX2) + y2(x + -1) * dy = 0
(-1dxX2 + dxyX2) + y2(x + -1) * dy = 0

Reorder the terms:
-1dxX2 + dxyX2 + y2(-1 + x) * dy = 0

Reorder the terms for easier multiplication:
-1dxX2 + dxyX2 + y2 * dy(-1 + x) = 0

Multiply y2 * dy
-1dxX2 + dxyX2 + dy3(-1 + x) = 0
-1dxX2 + dxyX2 + (-1 * dy3 + x * dy3) = 0

Reorder the terms:
-1dxX2 + dxyX2 + (dxy3 + -1dy3) = 0
-1dxX2 + dxyX2 + (dxy3 + -1dy3) = 0

Solving
-1dxX2 + dxyX2 + dxy3 + -1dy3 = 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(-1xX2 + xyX2 + xy3 + -1y3) = 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 '(-1xX2 + xyX2 + xy3 + -1y3)' equal to zero and attempt to solve:

Simplifying
-1xX2 + xyX2 + xy3 + -1y3 = 0

Solving
-1xX2 + xyX2 + xy3 + -1y3 = 0

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

Add 'xX2' to each side of the equation.
-1xX2 + xyX2 + xy3 + xX2 + -1y3 = 0 + xX2

Reorder the terms:
-1xX2 + xX2 + xyX2 + xy3 + -1y3 = 0 + xX2

Combine like terms: -1xX2 + xX2 = 0
0 + xyX2 + xy3 + -1y3 = 0 + xX2
xyX2 + xy3 + -1y3 = 0 + xX2
Remove the zero:
xyX2 + xy3 + -1y3 = xX2

Add '-1xyX2' to each side of the equation.
xyX2 + xy3 + -1xyX2 + -1y3 = xX2 + -1xyX2

Reorder the terms:
xyX2 + -1xyX2 + xy3 + -1y3 = xX2 + -1xyX2

Combine like terms: xyX2 + -1xyX2 = 0
0 + xy3 + -1y3 = xX2 + -1xyX2
xy3 + -1y3 = xX2 + -1xyX2

Add '-1xy3' to each side of the equation.
xy3 + -1xy3 + -1y3 = xX2 + -1xyX2 + -1xy3

Combine like terms: xy3 + -1xy3 = 0
0 + -1y3 = xX2 + -1xyX2 + -1xy3
-1y3 = xX2 + -1xyX2 + -1xy3

Add 'y3' to each side of the equation.
-1y3 + y3 = xX2 + -1xyX2 + -1xy3 + y3

Combine like terms: -1y3 + y3 = 0
0 = xX2 + -1xyX2 + -1xy3 + y3

Simplifying
0 = xX2 + -1xyX2 + -1xy3 + y3

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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