(y-2)dx-(x-y-1)dy=0

Solution for (y-2)dx-(x-y-1)dy=0 equation:

Simplifying
(y + -2) * dx + -1(x + -1y + -1) * dy = 0

Reorder the terms:
(-2 + y) * dx + -1(x + -1y + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(-2 + y) + -1(x + -1y + -1) * dy = 0
(-2 * dx + y * dx) + -1(x + -1y + -1) * dy = 0
(-2dx + dxy) + -1(x + -1y + -1) * dy = 0

Reorder the terms:
-2dx + dxy + -1(-1 + x + -1y) * dy = 0

Reorder the terms for easier multiplication:
-2dx + dxy + -1dy(-1 + x + -1y) = 0
-2dx + dxy + (-1 * -1dy + x * -1dy + -1y * -1dy) = 0

Reorder the terms:
-2dx + dxy + (-1dxy + 1dy + 1dy2) = 0
-2dx + dxy + (-1dxy + 1dy + 1dy2) = 0

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

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

Simplifying
-2x + y + y2 = 0

Solving
-2x + y + y2 = 0

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

Add '2x' to each side of the equation.
-2x + y + 2x + y2 = 0 + 2x

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

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

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

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

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

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

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