(2x+y-1)dx+(x-2y+3)dy=0

Solution for (2x+y-1)dx+(x-2y+3)dy=0 equation:

Simplifying
(2x + y + -1) * dx + (x + -2y + 3) * dy = 0

Reorder the terms:
(-1 + 2x + y) * dx + (x + -2y + 3) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 2x + y) + (x + -2y + 3) * dy = 0
(-1 * dx + 2x * dx + y * dx) + (x + -2y + 3) * dy = 0

Reorder the terms:
(-1dx + dxy + 2dx2) + (x + -2y + 3) * dy = 0
(-1dx + dxy + 2dx2) + (x + -2y + 3) * dy = 0

Reorder the terms:
-1dx + dxy + 2dx2 + (3 + x + -2y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + dxy + 2dx2 + dy(3 + x + -2y) = 0
-1dx + dxy + 2dx2 + (3 * dy + x * dy + -2y * dy) = 0

Reorder the terms:
-1dx + dxy + 2dx2 + (dxy + 3dy + -2dy2) = 0
-1dx + dxy + 2dx2 + (dxy + 3dy + -2dy2) = 0

Reorder the terms:
-1dx + dxy + dxy + 2dx2 + 3dy + -2dy2 = 0

Combine like terms: dxy + dxy = 2dxy
-1dx + 2dxy + 2dx2 + 3dy + -2dy2 = 0

Solving
-1dx + 2dxy + 2dx2 + 3dy + -2dy2 = 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 + 2x2 + 3y + -2y2) = 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 + 2x2 + 3y + -2y2)' equal to zero and attempt to solve:

Simplifying
-1x + 2xy + 2x2 + 3y + -2y2 = 0

Solving
-1x + 2xy + 2x2 + 3y + -2y2 = 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 + 2x2 + 3y + x + -2y2 = 0 + x

Reorder the terms:
-1x + x + 2xy + 2x2 + 3y + -2y2 = 0 + x

Combine like terms: -1x + x = 0
0 + 2xy + 2x2 + 3y + -2y2 = 0 + x
2xy + 2x2 + 3y + -2y2 = 0 + x
Remove the zero:
2xy + 2x2 + 3y + -2y2 = x

Add '-2xy' to each side of the equation.
2xy + 2x2 + 3y + -2xy + -2y2 = x + -2xy

Reorder the terms:
2xy + -2xy + 2x2 + 3y + -2y2 = x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 2x2 + 3y + -2y2 = x + -2xy
2x2 + 3y + -2y2 = x + -2xy

Add '-2x2' to each side of the equation.
2x2 + 3y + -2x2 + -2y2 = x + -2xy + -2x2

Reorder the terms:
2x2 + -2x2 + 3y + -2y2 = x + -2xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 3y + -2y2 = x + -2xy + -2x2
3y + -2y2 = x + -2xy + -2x2

Add '-3y' to each side of the equation.
3y + -3y + -2y2 = x + -2xy + -2x2 + -3y

Combine like terms: 3y + -3y = 0
0 + -2y2 = x + -2xy + -2x2 + -3y
-2y2 = x + -2xy + -2x2 + -3y

Add '2y2' to each side of the equation.
-2y2 + 2y2 = x + -2xy + -2x2 + -3y + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = x + -2xy + -2x2 + -3y + 2y2

Simplifying
0 = x + -2xy + -2x2 + -3y + 2y2

The solution to this equation could not be determined.

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