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

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

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

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

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

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

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

Combine like terms: dxy + -1dxy = 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(-1x + 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 '(-1x + y)' equal to zero and attempt to solve:

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

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

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

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

Simplifying
0 = x + -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}