(4x^3-2y)dx+(2y^3-2x)dy=0

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Solution for (4x^3-2y)dx+(2y^3-2x)dy=0 equation: 


Simplifying
(4x3 + -2y) * dx + (2y3 + -2x) * dy = 0

Reorder the terms for easier multiplication:
dx(4x3 + -2y) + (2y3 + -2x) * dy = 0
(4x3 * dx + -2y * dx) + (2y3 + -2x) * dy = 0

Reorder the terms:
(-2dxy + 4dx4) + (2y3 + -2x) * dy = 0
(-2dxy + 4dx4) + (2y3 + -2x) * dy = 0

Reorder the terms:
-2dxy + 4dx4 + (-2x + 2y3) * dy = 0

Reorder the terms for easier multiplication:
-2dxy + 4dx4 + dy(-2x + 2y3) = 0
-2dxy + 4dx4 + (-2x * dy + 2y3 * dy) = 0
-2dxy + 4dx4 + (-2dxy + 2dy4) = 0

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

Combine like terms: -2dxy + -2dxy = -4dxy
-4dxy + 4dx4 + 2dy4 = 0

Solving
-4dxy + 4dx4 + 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(-2xy + 2x4 + 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 '(-2xy + 2x4 + y4)' equal to zero and attempt to solve:

Simplifying
-2xy + 2x4 + y4 = 0

Solving
-2xy + 2x4 + y4 = 0

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

Add '2xy' to each side of the equation.
-2xy + 2x4 + 2xy + y4 = 0 + 2xy

Reorder the terms:
-2xy + 2xy + 2x4 + y4 = 0 + 2xy

Combine like terms: -2xy + 2xy = 0
0 + 2x4 + y4 = 0 + 2xy
2x4 + y4 = 0 + 2xy
Remove the zero:
2x4 + y4 = 2xy

Add '-2x4' to each side of the equation.
2x4 + -2x4 + y4 = 2xy + -2x4

Combine like terms: 2x4 + -2x4 = 0
0 + y4 = 2xy + -2x4
y4 = 2xy + -2x4

Add '-1y4' to each side of the equation.
y4 + -1y4 = 2xy + -2x4 + -1y4

Combine like terms: y4 + -1y4 = 0
0 = 2xy + -2x4 + -1y4

Simplifying
0 = 2xy + -2x4 + -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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