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

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


Simplifying
(4x3y + y3 + -2x) * dx + (x4 + 3xy2 + -3y2) * dy = 0

Reorder the terms:
(-2x + 4x3y + y3) * dx + (x4 + 3xy2 + -3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(-2x + 4x3y + y3) + (x4 + 3xy2 + -3y2) * dy = 0
(-2x * dx + 4x3y * dx + y3 * dx) + (x4 + 3xy2 + -3y2) * dy = 0

Reorder the terms:
(dxy3 + -2dx2 + 4dx4y) + (x4 + 3xy2 + -3y2) * dy = 0
(dxy3 + -2dx2 + 4dx4y) + (x4 + 3xy2 + -3y2) * dy = 0

Reorder the terms:
dxy3 + -2dx2 + 4dx4y + (3xy2 + x4 + -3y2) * dy = 0

Reorder the terms for easier multiplication:
dxy3 + -2dx2 + 4dx4y + dy(3xy2 + x4 + -3y2) = 0
dxy3 + -2dx2 + 4dx4y + (3xy2 * dy + x4 * dy + -3y2 * dy) = 0
dxy3 + -2dx2 + 4dx4y + (3dxy3 + dx4y + -3dy3) = 0

Reorder the terms:
dxy3 + 3dxy3 + -2dx2 + 4dx4y + dx4y + -3dy3 = 0

Combine like terms: dxy3 + 3dxy3 = 4dxy3
4dxy3 + -2dx2 + 4dx4y + dx4y + -3dy3 = 0

Combine like terms: 4dx4y + dx4y = 5dx4y
4dxy3 + -2dx2 + 5dx4y + -3dy3 = 0

Solving
4dxy3 + -2dx2 + 5dx4y + -3dy3 = 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(4xy3 + -2x2 + 5x4y + -3y3) = 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 '(4xy3 + -2x2 + 5x4y + -3y3)' equal to zero and attempt to solve:

Simplifying
4xy3 + -2x2 + 5x4y + -3y3 = 0

Solving
4xy3 + -2x2 + 5x4y + -3y3 = 0

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

Add '-4xy3' to each side of the equation.
4xy3 + -2x2 + 5x4y + -4xy3 + -3y3 = 0 + -4xy3

Reorder the terms:
4xy3 + -4xy3 + -2x2 + 5x4y + -3y3 = 0 + -4xy3

Combine like terms: 4xy3 + -4xy3 = 0
0 + -2x2 + 5x4y + -3y3 = 0 + -4xy3
-2x2 + 5x4y + -3y3 = 0 + -4xy3
Remove the zero:
-2x2 + 5x4y + -3y3 = -4xy3

Add '2x2' to each side of the equation.
-2x2 + 5x4y + 2x2 + -3y3 = -4xy3 + 2x2

Reorder the terms:
-2x2 + 2x2 + 5x4y + -3y3 = -4xy3 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + 5x4y + -3y3 = -4xy3 + 2x2
5x4y + -3y3 = -4xy3 + 2x2

Add '-5x4y' to each side of the equation.
5x4y + -5x4y + -3y3 = -4xy3 + 2x2 + -5x4y

Combine like terms: 5x4y + -5x4y = 0
0 + -3y3 = -4xy3 + 2x2 + -5x4y
-3y3 = -4xy3 + 2x2 + -5x4y

Add '3y3' to each side of the equation.
-3y3 + 3y3 = -4xy3 + 2x2 + -5x4y + 3y3

Combine like terms: -3y3 + 3y3 = 0
0 = -4xy3 + 2x2 + -5x4y + 3y3

Simplifying
0 = -4xy3 + 2x2 + -5x4y + 3y3

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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