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

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

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

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

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

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

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

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

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

Solving
1dx + -2dxy + 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 + -2xy + y) = 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 + -2xy + y)' equal to zero and attempt to solve:

Simplifying
x + -2xy + y = 0

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

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

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

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

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

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

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

Simplifying
0 = -1x + 2xy + -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}