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

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

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

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

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

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

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

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

Solving
1dx + 2dxy + 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 + 2xy + 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 + 2xy + y)' equal to zero and attempt to solve:

Simplifying
x + 2xy + y = 0

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

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

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

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

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

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

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

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