(X^3+Y^3)dx+(X^2-2XY)dy=0

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Solution for (X^3+Y^3)dx+(X^2-2XY)dy=0 equation: 


Simplifying
(X3 + Y3) * dx + (X2 + -2XY) * dy = 0

Reorder the terms for easier multiplication:
dx(X3 + Y3) + (X2 + -2XY) * dy = 0
(X3 * dx + Y3 * dx) + (X2 + -2XY) * dy = 0
(dxX3 + dxY3) + (X2 + -2XY) * dy = 0

Reorder the terms:
dxX3 + dxY3 + (-2XY + X2) * dy = 0

Reorder the terms for easier multiplication:
dxX3 + dxY3 + dy(-2XY + X2) = 0
dxX3 + dxY3 + (-2XY * dy + X2 * dy) = 0
dxX3 + dxY3 + (-2dyXY + dyX2) = 0

Solving
dxX3 + dxY3 + -2dyXY + dyX2 = 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(xX3 + xY3 + -2yXY + yX2) = 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 '(xX3 + xY3 + -2yXY + yX2)' equal to zero and attempt to solve:

Simplifying
xX3 + xY3 + -2yXY + yX2 = 0

Solving
xX3 + xY3 + -2yXY + yX2 = 0

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

Add '-1xX3' to each side of the equation.
xX3 + xY3 + -2yXY + -1xX3 + yX2 = 0 + -1xX3

Reorder the terms:
xX3 + -1xX3 + xY3 + -2yXY + yX2 = 0 + -1xX3

Combine like terms: xX3 + -1xX3 = 0
0 + xY3 + -2yXY + yX2 = 0 + -1xX3
xY3 + -2yXY + yX2 = 0 + -1xX3
Remove the zero:
xY3 + -2yXY + yX2 = -1xX3

Add '-1xY3' to each side of the equation.
xY3 + -2yXY + -1xY3 + yX2 = -1xX3 + -1xY3

Reorder the terms:
xY3 + -1xY3 + -2yXY + yX2 = -1xX3 + -1xY3

Combine like terms: xY3 + -1xY3 = 0
0 + -2yXY + yX2 = -1xX3 + -1xY3
-2yXY + yX2 = -1xX3 + -1xY3

Add '2yXY' to each side of the equation.
-2yXY + 2yXY + yX2 = -1xX3 + -1xY3 + 2yXY

Combine like terms: -2yXY + 2yXY = 0
0 + yX2 = -1xX3 + -1xY3 + 2yXY
yX2 = -1xX3 + -1xY3 + 2yXY

Add '-1yX2' to each side of the equation.
yX2 + -1yX2 = -1xX3 + -1xY3 + 2yXY + -1yX2

Combine like terms: yX2 + -1yX2 = 0
0 = -1xX3 + -1xY3 + 2yXY + -1yX2

Simplifying
0 = -1xX3 + -1xY3 + 2yXY + -1yX2

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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