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

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


Simplifying
(2x + y3) * dx + (3xy2 + 4) * dy = 0

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

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

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

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

Reorder the terms:
dxy3 + 2dx2 + (3dxy3 + 4dy) = 0
dxy3 + 2dx2 + (3dxy3 + 4dy) = 0

Reorder the terms:
dxy3 + 3dxy3 + 2dx2 + 4dy = 0

Combine like terms: dxy3 + 3dxy3 = 4dxy3
4dxy3 + 2dx2 + 4dy = 0

Solving
4dxy3 + 2dx2 + 4dy = 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(2xy3 + x2 + 2y) = 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 '(2xy3 + x2 + 2y)' equal to zero and attempt to solve:

Simplifying
2xy3 + x2 + 2y = 0

Solving
2xy3 + x2 + 2y = 0

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

Add '-2xy3' to each side of the equation.
2xy3 + x2 + -2xy3 + 2y = 0 + -2xy3

Reorder the terms:
2xy3 + -2xy3 + x2 + 2y = 0 + -2xy3

Combine like terms: 2xy3 + -2xy3 = 0
0 + x2 + 2y = 0 + -2xy3
x2 + 2y = 0 + -2xy3
Remove the zero:
x2 + 2y = -2xy3

Add '-1x2' to each side of the equation.
x2 + -1x2 + 2y = -2xy3 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 2y = -2xy3 + -1x2
2y = -2xy3 + -1x2

Add '-2y' to each side of the equation.
2y + -2y = -2xy3 + -1x2 + -2y

Combine like terms: 2y + -2y = 0
0 = -2xy3 + -1x2 + -2y

Simplifying
0 = -2xy3 + -1x2 + -2y

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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