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

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


Simplifying
(3x2 + -1y) * dx + (3y2 + -1x) * dy = 0

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

Reorder the terms:
(-1dxy + 3dx3) + (3y2 + -1x) * dy = 0
(-1dxy + 3dx3) + (3y2 + -1x) * dy = 0

Reorder the terms:
-1dxy + 3dx3 + (-1x + 3y2) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + 3dx3 + dy(-1x + 3y2) = 0
-1dxy + 3dx3 + (-1x * dy + 3y2 * dy) = 0
-1dxy + 3dx3 + (-1dxy + 3dy3) = 0

Reorder the terms:
-1dxy + -1dxy + 3dx3 + 3dy3 = 0

Combine like terms: -1dxy + -1dxy = -2dxy
-2dxy + 3dx3 + 3dy3 = 0

Solving
-2dxy + 3dx3 + 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(-2xy + 3x3 + 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 '(-2xy + 3x3 + 3y3)' equal to zero and attempt to solve:

Simplifying
-2xy + 3x3 + 3y3 = 0

Solving
-2xy + 3x3 + 3y3 = 0

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

Add '2xy' to each side of the equation.
-2xy + 3x3 + 2xy + 3y3 = 0 + 2xy

Reorder the terms:
-2xy + 2xy + 3x3 + 3y3 = 0 + 2xy

Combine like terms: -2xy + 2xy = 0
0 + 3x3 + 3y3 = 0 + 2xy
3x3 + 3y3 = 0 + 2xy
Remove the zero:
3x3 + 3y3 = 2xy

Add '-3x3' to each side of the equation.
3x3 + -3x3 + 3y3 = 2xy + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 3y3 = 2xy + -3x3
3y3 = 2xy + -3x3

Add '-3y3' to each side of the equation.
3y3 + -3y3 = 2xy + -3x3 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = 2xy + -3x3 + -3y3

Simplifying
0 = 2xy + -3x3 + -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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