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

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


Simplifying
(x3 + 3xy2) * dx + (3x2y + y3) * dy = 0

Reorder the terms:
(3xy2 + x3) * dx + (3x2y + y3) * dy = 0

Reorder the terms for easier multiplication:
dx(3xy2 + x3) + (3x2y + y3) * dy = 0
(3xy2 * dx + x3 * dx) + (3x2y + y3) * dy = 0
(3dx2y2 + dx4) + (3x2y + y3) * dy = 0

Reorder the terms for easier multiplication:
3dx2y2 + dx4 + dy(3x2y + y3) = 0
3dx2y2 + dx4 + (3x2y * dy + y3 * dy) = 0
3dx2y2 + dx4 + (3dx2y2 + dy4) = 0

Reorder the terms:
3dx2y2 + 3dx2y2 + dx4 + dy4 = 0

Combine like terms: 3dx2y2 + 3dx2y2 = 6dx2y2
6dx2y2 + dx4 + dy4 = 0

Solving
6dx2y2 + dx4 + dy4 = 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(6x2y2 + x4 + y4) = 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 '(6x2y2 + x4 + y4)' equal to zero and attempt to solve:

Simplifying
6x2y2 + x4 + y4 = 0

Solving
6x2y2 + x4 + y4 = 0

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

Add '-6x2y2' to each side of the equation.
6x2y2 + x4 + -6x2y2 + y4 = 0 + -6x2y2

Reorder the terms:
6x2y2 + -6x2y2 + x4 + y4 = 0 + -6x2y2

Combine like terms: 6x2y2 + -6x2y2 = 0
0 + x4 + y4 = 0 + -6x2y2
x4 + y4 = 0 + -6x2y2
Remove the zero:
x4 + y4 = -6x2y2

Add '-1x4' to each side of the equation.
x4 + -1x4 + y4 = -6x2y2 + -1x4

Combine like terms: x4 + -1x4 = 0
0 + y4 = -6x2y2 + -1x4
y4 = -6x2y2 + -1x4

Add '-1y4' to each side of the equation.
y4 + -1y4 = -6x2y2 + -1x4 + -1y4

Combine like terms: y4 + -1y4 = 0
0 = -6x2y2 + -1x4 + -1y4

Simplifying
0 = -6x2y2 + -1x4 + -1y4

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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