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

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


Simplifying
(3x2y + 2y + 3) * dx + (x3 + 2x + 3y2) * dy = 0

Reorder the terms:
(3 + 3x2y + 2y) * dx + (x3 + 2x + 3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 3x2y + 2y) + (x3 + 2x + 3y2) * dy = 0
(3 * dx + 3x2y * dx + 2y * dx) + (x3 + 2x + 3y2) * dy = 0

Reorder the terms:
(3dx + 2dxy + 3dx3y) + (x3 + 2x + 3y2) * dy = 0
(3dx + 2dxy + 3dx3y) + (x3 + 2x + 3y2) * dy = 0

Reorder the terms:
3dx + 2dxy + 3dx3y + (2x + x3 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
3dx + 2dxy + 3dx3y + dy(2x + x3 + 3y2) = 0
3dx + 2dxy + 3dx3y + (2x * dy + x3 * dy + 3y2 * dy) = 0
3dx + 2dxy + 3dx3y + (2dxy + dx3y + 3dy3) = 0

Reorder the terms:
3dx + 2dxy + 2dxy + 3dx3y + dx3y + 3dy3 = 0

Combine like terms: 2dxy + 2dxy = 4dxy
3dx + 4dxy + 3dx3y + dx3y + 3dy3 = 0

Combine like terms: 3dx3y + dx3y = 4dx3y
3dx + 4dxy + 4dx3y + 3dy3 = 0

Solving
3dx + 4dxy + 4dx3y + 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(3x + 4xy + 4x3y + 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 '(3x + 4xy + 4x3y + 3y3)' equal to zero and attempt to solve:

Simplifying
3x + 4xy + 4x3y + 3y3 = 0

Solving
3x + 4xy + 4x3y + 3y3 = 0

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

Add '-3x' to each side of the equation.
3x + 4xy + 4x3y + -3x + 3y3 = 0 + -3x

Reorder the terms:
3x + -3x + 4xy + 4x3y + 3y3 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 4xy + 4x3y + 3y3 = 0 + -3x
4xy + 4x3y + 3y3 = 0 + -3x
Remove the zero:
4xy + 4x3y + 3y3 = -3x

Add '-4xy' to each side of the equation.
4xy + 4x3y + -4xy + 3y3 = -3x + -4xy

Reorder the terms:
4xy + -4xy + 4x3y + 3y3 = -3x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 4x3y + 3y3 = -3x + -4xy
4x3y + 3y3 = -3x + -4xy

Add '-4x3y' to each side of the equation.
4x3y + -4x3y + 3y3 = -3x + -4xy + -4x3y

Combine like terms: 4x3y + -4x3y = 0
0 + 3y3 = -3x + -4xy + -4x3y
3y3 = -3x + -4xy + -4x3y

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -3x + -4xy + -4x3y + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -3x + -4xy + -4x3y + -3y3

Simplifying
0 = -3x + -4xy + -4x3y + -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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