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

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

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

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

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

Reorder the terms:
(dxy + -1dy + dy2) = (x + y + 1) * dx
(dxy + -1dy + dy2) = (x + y + 1) * dx

Reorder the terms:
dxy + -1dy + dy2 = (1 + x + y) * dx

Reorder the terms for easier multiplication:
dxy + -1dy + dy2 = dx(1 + x + y)
dxy + -1dy + dy2 = (1 * dx + x * dx + y * dx)

Reorder the terms:
dxy + -1dy + dy2 = (1dx + dxy + dx2)
dxy + -1dy + dy2 = (1dx + dxy + dx2)

Add '-1dxy' to each side of the equation.
dxy + -1dy + -1dxy + dy2 = 1dx + dxy + -1dxy + dx2

Reorder the terms:
dxy + -1dxy + -1dy + dy2 = 1dx + dxy + -1dxy + dx2

Combine like terms: dxy + -1dxy = 0
0 + -1dy + dy2 = 1dx + dxy + -1dxy + dx2
-1dy + dy2 = 1dx + dxy + -1dxy + dx2

Combine like terms: dxy + -1dxy = 0
-1dy + dy2 = 1dx + 0 + dx2
-1dy + dy2 = 1dx + dx2

Solving
-1dy + dy2 = 1dx + dx2

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.
-1dy + -1dx + dy2 = 1dx + -1dx + dx2

Reorder the terms:
-1dx + -1dy + dy2 = 1dx + -1dx + dx2

Combine like terms: 1dx + -1dx = 0
-1dx + -1dy + dy2 = 0 + dx2
-1dx + -1dy + dy2 = dx2

Add '-1dx2' to each side of the equation.
-1dx + -1dy + -1dx2 + dy2 = dx2 + -1dx2

Reorder the terms:
-1dx + -1dx2 + -1dy + dy2 = dx2 + -1dx2

Combine like terms: dx2 + -1dx2 = 0
-1dx + -1dx2 + -1dy + dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1x + -1x2 + -1y + y2) = 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 '(-1x + -1x2 + -1y + y2)' equal to zero and attempt to solve:

Simplifying
-1x + -1x2 + -1y + y2 = 0

Solving
-1x + -1x2 + -1y + y2 = 0

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

Add 'x' to each side of the equation.
-1x + -1x2 + -1y + x + y2 = 0 + x

Reorder the terms:
-1x + x + -1x2 + -1y + y2 = 0 + x

Combine like terms: -1x + x = 0
0 + -1x2 + -1y + y2 = 0 + x
-1x2 + -1y + y2 = 0 + x
Remove the zero:
-1x2 + -1y + y2 = x

Add 'x2' to each side of the equation.
-1x2 + -1y + x2 + y2 = x + x2

Reorder the terms:
-1x2 + x2 + -1y + y2 = x + x2

Combine like terms: -1x2 + x2 = 0
0 + -1y + y2 = x + x2
-1y + y2 = x + x2

Add 'y' to each side of the equation.
-1y + y + y2 = x + x2 + y

Combine like terms: -1y + y = 0
0 + y2 = x + x2 + y
y2 = x + x2 + y

Add '-1y2' to each side of the equation.
y2 + -1y2 = x + x2 + y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = x + x2 + y + -1y2

Simplifying
0 = x + x2 + y + -1y2

The solution to this equation could not be determined.

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