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

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


Simplifying
(2x3 + -2xy + y2) * dx + 2(xy + -1x2 + -2y3) * dy = 0

Reorder the terms:
(-2xy + 2x3 + y2) * dx + 2(xy + -1x2 + -2y3) * dy = 0

Reorder the terms for easier multiplication:
dx(-2xy + 2x3 + y2) + 2(xy + -1x2 + -2y3) * dy = 0
(-2xy * dx + 2x3 * dx + y2 * dx) + 2(xy + -1x2 + -2y3) * dy = 0

Reorder the terms:
(dxy2 + -2dx2y + 2dx4) + 2(xy + -1x2 + -2y3) * dy = 0
(dxy2 + -2dx2y + 2dx4) + 2(xy + -1x2 + -2y3) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + -2dx2y + 2dx4 + 2dy(xy + -1x2 + -2y3) = 0
dxy2 + -2dx2y + 2dx4 + (xy * 2dy + -1x2 * 2dy + -2y3 * 2dy) = 0
dxy2 + -2dx2y + 2dx4 + (2dxy2 + -2dx2y + -4dy4) = 0

Reorder the terms:
dxy2 + 2dxy2 + -2dx2y + -2dx2y + 2dx4 + -4dy4 = 0

Combine like terms: dxy2 + 2dxy2 = 3dxy2
3dxy2 + -2dx2y + -2dx2y + 2dx4 + -4dy4 = 0

Combine like terms: -2dx2y + -2dx2y = -4dx2y
3dxy2 + -4dx2y + 2dx4 + -4dy4 = 0

Solving
3dxy2 + -4dx2y + 2dx4 + -4dy4 = 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(3xy2 + -4x2y + 2x4 + -4y4) = 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 '(3xy2 + -4x2y + 2x4 + -4y4)' equal to zero and attempt to solve:

Simplifying
3xy2 + -4x2y + 2x4 + -4y4 = 0

Solving
3xy2 + -4x2y + 2x4 + -4y4 = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + -4x2y + 2x4 + -3xy2 + -4y4 = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + -4x2y + 2x4 + -4y4 = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + -4x2y + 2x4 + -4y4 = 0 + -3xy2
-4x2y + 2x4 + -4y4 = 0 + -3xy2
Remove the zero:
-4x2y + 2x4 + -4y4 = -3xy2

Add '4x2y' to each side of the equation.
-4x2y + 2x4 + 4x2y + -4y4 = -3xy2 + 4x2y

Reorder the terms:
-4x2y + 4x2y + 2x4 + -4y4 = -3xy2 + 4x2y

Combine like terms: -4x2y + 4x2y = 0
0 + 2x4 + -4y4 = -3xy2 + 4x2y
2x4 + -4y4 = -3xy2 + 4x2y

Add '-2x4' to each side of the equation.
2x4 + -2x4 + -4y4 = -3xy2 + 4x2y + -2x4

Combine like terms: 2x4 + -2x4 = 0
0 + -4y4 = -3xy2 + 4x2y + -2x4
-4y4 = -3xy2 + 4x2y + -2x4

Add '4y4' to each side of the equation.
-4y4 + 4y4 = -3xy2 + 4x2y + -2x4 + 4y4

Combine like terms: -4y4 + 4y4 = 0
0 = -3xy2 + 4x2y + -2x4 + 4y4

Simplifying
0 = -3xy2 + 4x2y + -2x4 + 4y4

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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