(y-x-1)dx+(x+y-1)dy=0I

Solution for (y-x-1)dx+(x+y-1)dy=0I equation:

Simplifying
(y + -1x + -1) * dx + (x + y + -1) * dy = 0I

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

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

Reorder the terms:
(-1dx + dxy + -1dx2) + (x + y + -1) * dy = 0I
(-1dx + dxy + -1dx2) + (x + y + -1) * dy = 0I

Reorder the terms:
-1dx + dxy + -1dx2 + (-1 + x + y) * dy = 0I

Reorder the terms for easier multiplication:
-1dx + dxy + -1dx2 + dy(-1 + x + y) = 0I
-1dx + dxy + -1dx2 + (-1 * dy + x * dy + y * dy) = 0I

Reorder the terms:
-1dx + dxy + -1dx2 + (dxy + -1dy + dy2) = 0I
-1dx + dxy + -1dx2 + (dxy + -1dy + dy2) = 0I

Reorder the terms:
-1dx + dxy + dxy + -1dx2 + -1dy + dy2 = 0I

Combine like terms: dxy + dxy = 2dxy
-1dx + 2dxy + -1dx2 + -1dy + dy2 = 0I

Anything times zero is zero.
-1dx + 2dxy + -1dx2 + -1dy + dy2 = 0I

Solving
-1dx + 2dxy + -1dx2 + -1dy + dy2 = 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(-1x + 2xy + -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 + 2xy + -1x2 + -1y + y2)' equal to zero and attempt to solve:

Simplifying
-1x + 2xy + -1x2 + -1y + y2 = 0

Solving
-1x + 2xy + -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 + 2xy + -1x2 + -1y + x + y2 = 0 + x

Reorder the terms:
-1x + x + 2xy + -1x2 + -1y + y2 = 0 + x

Combine like terms: -1x + x = 0
0 + 2xy + -1x2 + -1y + y2 = 0 + x
2xy + -1x2 + -1y + y2 = 0 + x
Remove the zero:
2xy + -1x2 + -1y + y2 = x

Add '-2xy' to each side of the equation.
2xy + -1x2 + -1y + -2xy + y2 = x + -2xy

Reorder the terms:
2xy + -2xy + -1x2 + -1y + y2 = x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + -1x2 + -1y + y2 = x + -2xy
-1x2 + -1y + y2 = x + -2xy

Add 'x2' to each side of the equation.
-1x2 + -1y + x2 + y2 = x + -2xy + x2

Reorder the terms:
-1x2 + x2 + -1y + y2 = x + -2xy + x2

Combine like terms: -1x2 + x2 = 0
0 + -1y + y2 = x + -2xy + x2
-1y + y2 = x + -2xy + x2

Add 'y' to each side of the equation.
-1y + y + y2 = x + -2xy + x2 + y

Combine like terms: -1y + y = 0
0 + y2 = x + -2xy + x2 + y
y2 = x + -2xy + x2 + y

Add '-1y2' to each side of the equation.
y2 + -1y2 = x + -2xy + x2 + y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = x + -2xy + x2 + y + -1y2

Simplifying
0 = x + -2xy + 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}