(X^3-3xy^2)dx+(y^3-3x^2y)dy=0

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Solution for (X^3-3xy^2)dx+(y^3-3x^2y)dy=0 equation: 


Simplifying
(X3 + -3xy2) * dx + (y3 + -3x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(X3 + -3xy2) + (y3 + -3x2y) * dy = 0
(X3 * dx + -3xy2 * dx) + (y3 + -3x2y) * dy = 0
(dxX3 + -3dx2y2) + (y3 + -3x2y) * dy = 0

Reorder the terms:
dxX3 + -3dx2y2 + (-3x2y + y3) * dy = 0

Reorder the terms for easier multiplication:
dxX3 + -3dx2y2 + dy(-3x2y + y3) = 0
dxX3 + -3dx2y2 + (-3x2y * dy + y3 * dy) = 0
dxX3 + -3dx2y2 + (-3dx2y2 + dy4) = 0

Combine like terms: -3dx2y2 + -3dx2y2 = -6dx2y2
dxX3 + -6dx2y2 + dy4 = 0

Solving
dxX3 + -6dx2y2 + dy4 = 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 + -6x2y2 + y4) = 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 + -6x2y2 + y4)' equal to zero and attempt to solve:

Simplifying
xX3 + -6x2y2 + y4 = 0

Solving
xX3 + -6x2y2 + y4 = 0

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

Add '-1xX3' to each side of the equation.
xX3 + -6x2y2 + -1xX3 + y4 = 0 + -1xX3

Reorder the terms:
xX3 + -1xX3 + -6x2y2 + y4 = 0 + -1xX3

Combine like terms: xX3 + -1xX3 = 0
0 + -6x2y2 + y4 = 0 + -1xX3
-6x2y2 + y4 = 0 + -1xX3
Remove the zero:
-6x2y2 + y4 = -1xX3

Add '6x2y2' to each side of the equation.
-6x2y2 + 6x2y2 + y4 = -1xX3 + 6x2y2

Combine like terms: -6x2y2 + 6x2y2 = 0
0 + y4 = -1xX3 + 6x2y2
y4 = -1xX3 + 6x2y2

Add '-1y4' to each side of the equation.
y4 + -1y4 = -1xX3 + 6x2y2 + -1y4

Combine like terms: y4 + -1y4 = 0
0 = -1xX3 + 6x2y2 + -1y4

Simplifying
0 = -1xX3 + 6x2y2 + -1y4

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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