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

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

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

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

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

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

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

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

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

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

Solving
1dx = -1dy

Solving for variable 'd'.

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

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

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

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}