(x-1)dy=(y+1)dx

Solution for (x-1)dy=(y+1)dx equation:

Simplifying
(x + -1) * dy = (y + 1) * dx

Reorder the terms:
(-1 + x) * dy = (y + 1) * dx

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

Reorder the terms:
(dxy + -1dy) = (y + 1) * dx
(dxy + -1dy) = (y + 1) * dx

Reorder the terms:
dxy + -1dy = (1 + y) * dx

Reorder the terms for easier multiplication:
dxy + -1dy = dx(1 + y)
dxy + -1dy = (1 * dx + y * dx)
dxy + -1dy = (1dx + dxy)

Add '-1dxy' to each side of the equation.
dxy + -1dxy + -1dy = 1dx + dxy + -1dxy

Combine like terms: dxy + -1dxy = 0
0 + -1dy = 1dx + dxy + -1dxy
-1dy = 1dx + dxy + -1dxy

Combine like terms: dxy + -1dxy = 0
-1dy = 1dx + 0
-1dy = 1dx

Solving
-1dy = 1dx

Solving for variable 'd'.

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

Add '-1dx' to each side of the equation.
-1dx + -1dy = 1dx + -1dx

Combine like terms: 1dx + -1dx = 0
-1dx + -1dy = 0

Factor out the Greatest Common Factor (GCF), '-1d'.
-1d(x + y) = 0

Ignore the factor -1.
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 + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

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

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

Simplifying
0 = -1x + -1y

The solution to this equation could not be determined.

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