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

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

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

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

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

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

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

Reorder the terms for easier multiplication:
2dxy + -3dy + dy2 + dx(1 + y) = 0
2dxy + -3dy + dy2 + (1 * dx + y * dx) = 0
2dxy + -3dy + dy2 + (1dx + dxy) = 0

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

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

Solving
1dx + 3dxy + -3dy + 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(x + 3xy + -3y + 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 '(x + 3xy + -3y + y2)' equal to zero and attempt to solve:

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

Solving
x + 3xy + -3y + y2 = 0

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

Add '-1x' to each side of the equation.
x + 3xy + -3y + -1x + y2 = 0 + -1x

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

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

Add '-3xy' to each side of the equation.
3xy + -3y + -3xy + y2 = -1x + -3xy

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

Combine like terms: 3xy + -3xy = 0
0 + -3y + y2 = -1x + -3xy
-3y + y2 = -1x + -3xy

Add '3y' to each side of the equation.
-3y + 3y + y2 = -1x + -3xy + 3y

Combine like terms: -3y + 3y = 0
0 + y2 = -1x + -3xy + 3y
y2 = -1x + -3xy + 3y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1x + -3xy + 3y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1x + -3xy + 3y + -1y2

Simplifying
0 = -1x + -3xy + 3y + -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}