(y+x^3y+2x^2)dx+(x+4xy^4+8y^3)dy=0

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Solution for (y+x^3y+2x^2)dx+(x+4xy^4+8y^3)dy=0 equation: 


Simplifying
(y + x3y + 2x2) * dx + (x + 4xy4 + 8y3) * dy = 0

Reorder the terms:
(2x2 + x3y + y) * dx + (x + 4xy4 + 8y3) * dy = 0

Reorder the terms for easier multiplication:
dx(2x2 + x3y + y) + (x + 4xy4 + 8y3) * dy = 0
(2x2 * dx + x3y * dx + y * dx) + (x + 4xy4 + 8y3) * dy = 0

Reorder the terms:
(dxy + 2dx3 + dx4y) + (x + 4xy4 + 8y3) * dy = 0
(dxy + 2dx3 + dx4y) + (x + 4xy4 + 8y3) * dy = 0

Reorder the terms for easier multiplication:
dxy + 2dx3 + dx4y + dy(x + 4xy4 + 8y3) = 0
dxy + 2dx3 + dx4y + (x * dy + 4xy4 * dy + 8y3 * dy) = 0
dxy + 2dx3 + dx4y + (dxy + 4dxy5 + 8dy4) = 0

Reorder the terms:
dxy + dxy + 4dxy5 + 2dx3 + dx4y + 8dy4 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + 4dxy5 + 2dx3 + dx4y + 8dy4 = 0

Solving
2dxy + 4dxy5 + 2dx3 + dx4y + 8dy4 = 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(2xy + 4xy5 + 2x3 + x4y + 8y4) = 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 '(2xy + 4xy5 + 2x3 + x4y + 8y4)' equal to zero and attempt to solve:

Simplifying
2xy + 4xy5 + 2x3 + x4y + 8y4 = 0

Solving
2xy + 4xy5 + 2x3 + x4y + 8y4 = 0

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

Add '-2xy' to each side of the equation.
2xy + 4xy5 + 2x3 + x4y + -2xy + 8y4 = 0 + -2xy

Reorder the terms:
2xy + -2xy + 4xy5 + 2x3 + x4y + 8y4 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 4xy5 + 2x3 + x4y + 8y4 = 0 + -2xy
4xy5 + 2x3 + x4y + 8y4 = 0 + -2xy
Remove the zero:
4xy5 + 2x3 + x4y + 8y4 = -2xy

Add '-4xy5' to each side of the equation.
4xy5 + 2x3 + x4y + -4xy5 + 8y4 = -2xy + -4xy5

Reorder the terms:
4xy5 + -4xy5 + 2x3 + x4y + 8y4 = -2xy + -4xy5

Combine like terms: 4xy5 + -4xy5 = 0
0 + 2x3 + x4y + 8y4 = -2xy + -4xy5
2x3 + x4y + 8y4 = -2xy + -4xy5

Add '-2x3' to each side of the equation.
2x3 + x4y + -2x3 + 8y4 = -2xy + -4xy5 + -2x3

Reorder the terms:
2x3 + -2x3 + x4y + 8y4 = -2xy + -4xy5 + -2x3

Combine like terms: 2x3 + -2x3 = 0
0 + x4y + 8y4 = -2xy + -4xy5 + -2x3
x4y + 8y4 = -2xy + -4xy5 + -2x3

Add '-1x4y' to each side of the equation.
x4y + -1x4y + 8y4 = -2xy + -4xy5 + -2x3 + -1x4y

Combine like terms: x4y + -1x4y = 0
0 + 8y4 = -2xy + -4xy5 + -2x3 + -1x4y
8y4 = -2xy + -4xy5 + -2x3 + -1x4y

Add '-8y4' to each side of the equation.
8y4 + -8y4 = -2xy + -4xy5 + -2x3 + -1x4y + -8y4

Combine like terms: 8y4 + -8y4 = 0
0 = -2xy + -4xy5 + -2x3 + -1x4y + -8y4

Simplifying
0 = -2xy + -4xy5 + -2x3 + -1x4y + -8y4

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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