(y^2-2xy+6x)dx+(-x^2-2xy+2)dy=0

Solution for (y^2-2xy+6x)dx+(-x^2-2xy+2)dy=0 equation:

Simplifying
(y2 + -2xy + 6x) * dx + (-1x2 + -2xy + 2) * dy = 0

Reorder the terms:
(6x + -2xy + y2) * dx + (-1x2 + -2xy + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(6x + -2xy + y2) + (-1x2 + -2xy + 2) * dy = 0
(6x * dx + -2xy * dx + y2 * dx) + (-1x2 + -2xy + 2) * dy = 0

Reorder the terms:
(dxy2 + 6dx2 + -2dx2y) + (-1x2 + -2xy + 2) * dy = 0
(dxy2 + 6dx2 + -2dx2y) + (-1x2 + -2xy + 2) * dy = 0

Reorder the terms:
dxy2 + 6dx2 + -2dx2y + (2 + -2xy + -1x2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 6dx2 + -2dx2y + dy(2 + -2xy + -1x2) = 0
dxy2 + 6dx2 + -2dx2y + (2 * dy + -2xy * dy + -1x2 * dy) = 0

Reorder the terms:
dxy2 + 6dx2 + -2dx2y + (-2dxy2 + -1dx2y + 2dy) = 0
dxy2 + 6dx2 + -2dx2y + (-2dxy2 + -1dx2y + 2dy) = 0

Reorder the terms:
dxy2 + -2dxy2 + 6dx2 + -2dx2y + -1dx2y + 2dy = 0

Combine like terms: dxy2 + -2dxy2 = -1dxy2
-1dxy2 + 6dx2 + -2dx2y + -1dx2y + 2dy = 0

Combine like terms: -2dx2y + -1dx2y = -3dx2y
-1dxy2 + 6dx2 + -3dx2y + 2dy = 0

Solving
-1dxy2 + 6dx2 + -3dx2y + 2dy = 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(-1xy2 + 6x2 + -3x2y + 2y) = 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 '(-1xy2 + 6x2 + -3x2y + 2y)' equal to zero and attempt to solve:

Simplifying
-1xy2 + 6x2 + -3x2y + 2y = 0

Solving
-1xy2 + 6x2 + -3x2y + 2y = 0

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

Add 'xy2' to each side of the equation.
-1xy2 + 6x2 + -3x2y + xy2 + 2y = 0 + xy2

Reorder the terms:
-1xy2 + xy2 + 6x2 + -3x2y + 2y = 0 + xy2

Combine like terms: -1xy2 + xy2 = 0
0 + 6x2 + -3x2y + 2y = 0 + xy2
6x2 + -3x2y + 2y = 0 + xy2
Remove the zero:
6x2 + -3x2y + 2y = xy2

Add '-6x2' to each side of the equation.
6x2 + -3x2y + -6x2 + 2y = xy2 + -6x2

Reorder the terms:
6x2 + -6x2 + -3x2y + 2y = xy2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
0 + -3x2y + 2y = xy2 + -6x2
-3x2y + 2y = xy2 + -6x2

Add '3x2y' to each side of the equation.
-3x2y + 3x2y + 2y = xy2 + -6x2 + 3x2y

Combine like terms: -3x2y + 3x2y = 0
0 + 2y = xy2 + -6x2 + 3x2y
2y = xy2 + -6x2 + 3x2y

Add '-2y' to each side of the equation.
2y + -2y = xy2 + -6x2 + 3x2y + -2y

Combine like terms: 2y + -2y = 0
0 = xy2 + -6x2 + 3x2y + -2y

Simplifying
0 = xy2 + -6x2 + 3x2y + -2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}