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

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

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

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

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

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

Solving
1dx + dxy = -1dxy + 1dy

Solving for variable 'd'.

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

Add 'dxy' to each side of the equation.
1dx + dxy + dxy = -1dxy + dxy + 1dy

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

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

Add '-1dy' to each side of the equation.
1dx + 2dxy + -1dy = 1dy + -1dy

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + 2xy + -1y) = 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 + 2xy + -1y)' equal to zero and attempt to solve:

Simplifying
x + 2xy + -1y = 0

Solving
x + 2xy + -1y = 0

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

Add '-1x' to each side of the equation.
x + 2xy + -1x + -1y = 0 + -1x

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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