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

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


Simplifying
(3x2 + y2) * dx + (3x3 + -1y + 4xy) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + y2) + (3x3 + -1y + 4xy) * dy = 0
(3x2 * dx + y2 * dx) + (3x3 + -1y + 4xy) * dy = 0

Reorder the terms:
(dxy2 + 3dx3) + (3x3 + -1y + 4xy) * dy = 0
(dxy2 + 3dx3) + (3x3 + -1y + 4xy) * dy = 0

Reorder the terms:
dxy2 + 3dx3 + (4xy + 3x3 + -1y) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 3dx3 + dy(4xy + 3x3 + -1y) = 0
dxy2 + 3dx3 + (4xy * dy + 3x3 * dy + -1y * dy) = 0
dxy2 + 3dx3 + (4dxy2 + 3dx3y + -1dy2) = 0

Reorder the terms:
dxy2 + 4dxy2 + 3dx3 + 3dx3y + -1dy2 = 0

Combine like terms: dxy2 + 4dxy2 = 5dxy2
5dxy2 + 3dx3 + 3dx3y + -1dy2 = 0

Solving
5dxy2 + 3dx3 + 3dx3y + -1dy2 = 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(5xy2 + 3x3 + 3x3y + -1y2) = 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 '(5xy2 + 3x3 + 3x3y + -1y2)' equal to zero and attempt to solve:

Simplifying
5xy2 + 3x3 + 3x3y + -1y2 = 0

Solving
5xy2 + 3x3 + 3x3y + -1y2 = 0

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

Add '-5xy2' to each side of the equation.
5xy2 + 3x3 + 3x3y + -5xy2 + -1y2 = 0 + -5xy2

Reorder the terms:
5xy2 + -5xy2 + 3x3 + 3x3y + -1y2 = 0 + -5xy2

Combine like terms: 5xy2 + -5xy2 = 0
0 + 3x3 + 3x3y + -1y2 = 0 + -5xy2
3x3 + 3x3y + -1y2 = 0 + -5xy2
Remove the zero:
3x3 + 3x3y + -1y2 = -5xy2

Add '-3x3' to each side of the equation.
3x3 + 3x3y + -3x3 + -1y2 = -5xy2 + -3x3

Reorder the terms:
3x3 + -3x3 + 3x3y + -1y2 = -5xy2 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 3x3y + -1y2 = -5xy2 + -3x3
3x3y + -1y2 = -5xy2 + -3x3

Add '-3x3y' to each side of the equation.
3x3y + -3x3y + -1y2 = -5xy2 + -3x3 + -3x3y

Combine like terms: 3x3y + -3x3y = 0
0 + -1y2 = -5xy2 + -3x3 + -3x3y
-1y2 = -5xy2 + -3x3 + -3x3y

Add 'y2' to each side of the equation.
-1y2 + y2 = -5xy2 + -3x3 + -3x3y + y2

Combine like terms: -1y2 + y2 = 0
0 = -5xy2 + -3x3 + -3x3y + y2

Simplifying
0 = -5xy2 + -3x3 + -3x3y + y2

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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