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

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


Simplifying
(x3 + -3xy2 + 2) * dx + -1(3x2y + -1y2) * dy = 0

Reorder the terms:
(2 + -3xy2 + x3) * dx + -1(3x2y + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + -3xy2 + x3) + -1(3x2y + -1y2) * dy = 0
(2 * dx + -3xy2 * dx + x3 * dx) + -1(3x2y + -1y2) * dy = 0
(2dx + -3dx2y2 + dx4) + -1(3x2y + -1y2) * dy = 0

Reorder the terms for easier multiplication:
2dx + -3dx2y2 + dx4 + -1dy(3x2y + -1y2) = 0
2dx + -3dx2y2 + dx4 + (3x2y * -1dy + -1y2 * -1dy) = 0
2dx + -3dx2y2 + dx4 + (-3dx2y2 + 1dy3) = 0

Reorder the terms:
2dx + -3dx2y2 + -3dx2y2 + dx4 + 1dy3 = 0

Combine like terms: -3dx2y2 + -3dx2y2 = -6dx2y2
2dx + -6dx2y2 + dx4 + 1dy3 = 0

Solving
2dx + -6dx2y2 + dx4 + 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(2x + -6x2y2 + x4 + y3) = 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 '(2x + -6x2y2 + x4 + y3)' equal to zero and attempt to solve:

Simplifying
2x + -6x2y2 + x4 + y3 = 0

Solving
2x + -6x2y2 + x4 + y3 = 0

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

Add '-2x' to each side of the equation.
2x + -6x2y2 + x4 + -2x + y3 = 0 + -2x

Reorder the terms:
2x + -2x + -6x2y2 + x4 + y3 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + -6x2y2 + x4 + y3 = 0 + -2x
-6x2y2 + x4 + y3 = 0 + -2x
Remove the zero:
-6x2y2 + x4 + y3 = -2x

Add '6x2y2' to each side of the equation.
-6x2y2 + x4 + 6x2y2 + y3 = -2x + 6x2y2

Reorder the terms:
-6x2y2 + 6x2y2 + x4 + y3 = -2x + 6x2y2

Combine like terms: -6x2y2 + 6x2y2 = 0
0 + x4 + y3 = -2x + 6x2y2
x4 + y3 = -2x + 6x2y2

Add '-1x4' to each side of the equation.
x4 + -1x4 + y3 = -2x + 6x2y2 + -1x4

Combine like terms: x4 + -1x4 = 0
0 + y3 = -2x + 6x2y2 + -1x4
y3 = -2x + 6x2y2 + -1x4

Add '-1y3' to each side of the equation.
y3 + -1y3 = -2x + 6x2y2 + -1x4 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -2x + 6x2y2 + -1x4 + -1y3

Simplifying
0 = -2x + 6x2y2 + -1x4 + -1y3

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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