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

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

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

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

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

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

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

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

Solving
1dx + 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 + 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 + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

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

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

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

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

Simplifying
0 = -1x + -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}