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

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


Simplifying
(2x3 + -1xy2) * dx + (2y3 + -1x2y) * dy = 0

Reorder the terms:
(-1xy2 + 2x3) * dx + (2y3 + -1x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(-1xy2 + 2x3) + (2y3 + -1x2y) * dy = 0
(-1xy2 * dx + 2x3 * dx) + (2y3 + -1x2y) * dy = 0
(-1dx2y2 + 2dx4) + (2y3 + -1x2y) * dy = 0

Reorder the terms:
-1dx2y2 + 2dx4 + (-1x2y + 2y3) * dy = 0

Reorder the terms for easier multiplication:
-1dx2y2 + 2dx4 + dy(-1x2y + 2y3) = 0
-1dx2y2 + 2dx4 + (-1x2y * dy + 2y3 * dy) = 0
-1dx2y2 + 2dx4 + (-1dx2y2 + 2dy4) = 0

Reorder the terms:
-1dx2y2 + -1dx2y2 + 2dx4 + 2dy4 = 0

Combine like terms: -1dx2y2 + -1dx2y2 = -2dx2y2
-2dx2y2 + 2dx4 + 2dy4 = 0

Solving
-2dx2y2 + 2dx4 + 2dy4 = 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), '2d'.
2d(-1x2y2 + x4 + y4) = 0

Ignore the factor 2.

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 '(-1x2y2 + x4 + y4)' equal to zero and attempt to solve:

Simplifying
-1x2y2 + x4 + y4 = 0

Solving
-1x2y2 + x4 + y4 = 0

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

Add 'x2y2' to each side of the equation.
-1x2y2 + x4 + x2y2 + y4 = 0 + x2y2

Reorder the terms:
-1x2y2 + x2y2 + x4 + y4 = 0 + x2y2

Combine like terms: -1x2y2 + x2y2 = 0
0 + x4 + y4 = 0 + x2y2
x4 + y4 = 0 + x2y2
Remove the zero:
x4 + y4 = x2y2

Add '-1x4' to each side of the equation.
x4 + -1x4 + y4 = x2y2 + -1x4

Combine like terms: x4 + -1x4 = 0
0 + y4 = x2y2 + -1x4
y4 = x2y2 + -1x4

Add '-1y4' to each side of the equation.
y4 + -1y4 = x2y2 + -1x4 + -1y4

Combine like terms: y4 + -1y4 = 0
0 = x2y2 + -1x4 + -1y4

Simplifying
0 = x2y2 + -1x4 + -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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