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

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


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

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

Reorder the terms for easier multiplication:
dx(-2 + x) + (x + y + -1) * dy = 0
(-2 * dx + x * dx) + (x + y + -1) * dy = 0
(-2dx + dx2) + (x + y + -1) * dy = 0

Reorder the terms:
-2dx + dx2 + (-1 + x + y) * dy = 0

Reorder the terms for easier multiplication:
-2dx + dx2 + dy(-1 + x + y) = 0
-2dx + dx2 + (-1 * dy + x * dy + y * dy) = 0

Reorder the terms:
-2dx + dx2 + (dxy + -1dy + dy2) = 0
-2dx + dx2 + (dxy + -1dy + dy2) = 0

Reorder the terms:
-2dx + dxy + dx2 + -1dy + dy2 = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = 2x + -1xy + -1x2 + 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}

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