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

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


Simplifying
(3y2 + -1x) * dx + 2y(y2 + -3x) * dy = 0

Reorder the terms:
(-1x + 3y2) * dx + 2y(y2 + -3x) * dy = 0

Reorder the terms for easier multiplication:
dx(-1x + 3y2) + 2y(y2 + -3x) * dy = 0
(-1x * dx + 3y2 * dx) + 2y(y2 + -3x) * dy = 0

Reorder the terms:
(3dxy2 + -1dx2) + 2y(y2 + -3x) * dy = 0
(3dxy2 + -1dx2) + 2y(y2 + -3x) * dy = 0

Reorder the terms:
3dxy2 + -1dx2 + 2y(-3x + y2) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + -1dx2 + 2y * dy(-3x + y2) = 0

Multiply y * dy
3dxy2 + -1dx2 + 2dy2(-3x + y2) = 0
3dxy2 + -1dx2 + (-3x * 2dy2 + y2 * 2dy2) = 0
3dxy2 + -1dx2 + (-6dxy2 + 2dy4) = 0

Reorder the terms:
3dxy2 + -6dxy2 + -1dx2 + 2dy4 = 0

Combine like terms: 3dxy2 + -6dxy2 = -3dxy2
-3dxy2 + -1dx2 + 2dy4 = 0

Solving
-3dxy2 + -1dx2 + 2dy4 = 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(-3xy2 + -1x2 + 2y4) = 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 '(-3xy2 + -1x2 + 2y4)' equal to zero and attempt to solve:

Simplifying
-3xy2 + -1x2 + 2y4 = 0

Solving
-3xy2 + -1x2 + 2y4 = 0

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

Add '3xy2' to each side of the equation.
-3xy2 + -1x2 + 3xy2 + 2y4 = 0 + 3xy2

Reorder the terms:
-3xy2 + 3xy2 + -1x2 + 2y4 = 0 + 3xy2

Combine like terms: -3xy2 + 3xy2 = 0
0 + -1x2 + 2y4 = 0 + 3xy2
-1x2 + 2y4 = 0 + 3xy2
Remove the zero:
-1x2 + 2y4 = 3xy2

Add 'x2' to each side of the equation.
-1x2 + x2 + 2y4 = 3xy2 + x2

Combine like terms: -1x2 + x2 = 0
0 + 2y4 = 3xy2 + x2
2y4 = 3xy2 + x2

Add '-2y4' to each side of the equation.
2y4 + -2y4 = 3xy2 + x2 + -2y4

Combine like terms: 2y4 + -2y4 = 0
0 = 3xy2 + x2 + -2y4

Simplifying
0 = 3xy2 + x2 + -2y4

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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