(xy+1)dx+(xy-1)dy=0

Solution for (xy+1)dx+(xy-1)dy=0 equation:

Simplifying
(xy + 1) * dx + (xy + -1) * dy = 0

Reorder the terms:
(1 + xy) * dx + (xy + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + xy) + (xy + -1) * dy = 0
(1 * dx + xy * dx) + (xy + -1) * dy = 0
(1dx + dx2y) + (xy + -1) * dy = 0

Reorder the terms:
1dx + dx2y + (-1 + xy) * dy = 0

Reorder the terms for easier multiplication:
1dx + dx2y + dy(-1 + xy) = 0
1dx + dx2y + (-1 * dy + xy * dy) = 0

Reorder the terms:
1dx + dx2y + (dxy2 + -1dy) = 0
1dx + dx2y + (dxy2 + -1dy) = 0

Reorder the terms:
1dx + dxy2 + dx2y + -1dy = 0

Solving
1dx + dxy2 + dx2y + -1dy = 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(x + xy2 + x2y + -1y) = 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 '(x + xy2 + x2y + -1y)' equal to zero and attempt to solve:

Simplifying
x + xy2 + x2y + -1y = 0

Solving
x + xy2 + x2y + -1y = 0

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

Add '-1x' to each side of the equation.
x + xy2 + x2y + -1x + -1y = 0 + -1x

Reorder the terms:
x + -1x + xy2 + x2y + -1y = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy2 + x2y + -1y = 0 + -1x
xy2 + x2y + -1y = 0 + -1x
Remove the zero:
xy2 + x2y + -1y = -1x

Add '-1xy2' to each side of the equation.
xy2 + x2y + -1xy2 + -1y = -1x + -1xy2

Reorder the terms:
xy2 + -1xy2 + x2y + -1y = -1x + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x2y + -1y = -1x + -1xy2
x2y + -1y = -1x + -1xy2

Add '-1x2y' to each side of the equation.
x2y + -1x2y + -1y = -1x + -1xy2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + -1y = -1x + -1xy2 + -1x2y
-1y = -1x + -1xy2 + -1x2y

Add 'y' to each side of the equation.
-1y + y = -1x + -1xy2 + -1x2y + y

Combine like terms: -1y + y = 0
0 = -1x + -1xy2 + -1x2y + y

Simplifying
0 = -1x + -1xy2 + -1x2y + y

The solution to this equation could not be determined.

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