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

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

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

Multiply yX * dy
dy2X = (y + 1)(1 + -1x) * dx

Reorder the terms:
dy2X = (1 + y)(1 + -1x) * dx

Reorder the terms for easier multiplication:
dy2X = dx(1 + y)(1 + -1x)

Multiply (1 + y) * (1 + -1x)
dy2X = dx(1(1 + -1x) + y(1 + -1x))
dy2X = dx((1 * 1 + -1x * 1) + y(1 + -1x))
dy2X = dx((1 + -1x) + y(1 + -1x))
dy2X = dx(1 + -1x + (1 * y + -1x * y))

Reorder the terms:
dy2X = dx(1 + -1x + (-1xy + 1y))
dy2X = dx(1 + -1x + (-1xy + 1y))
dy2X = dx(1 + -1x + -1xy + 1y)
dy2X = (1 * dx + -1x * dx + -1xy * dx + 1y * dx)

Reorder the terms:
dy2X = (1dx + 1dxy + -1dx2 + -1dx2y)
dy2X = (1dx + 1dxy + -1dx2 + -1dx2y)

Solving
dy2X = 1dx + 1dxy + -1dx2 + -1dx2y

Solving for variable 'd'.

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

Add '-1dx' to each side of the equation.
-1dx + dy2X = 1dx + 1dxy + -1dx2 + -1dx + -1dx2y

Reorder the terms:
-1dx + dy2X = 1dx + -1dx + 1dxy + -1dx2 + -1dx2y

Combine like terms: 1dx + -1dx = 0
-1dx + dy2X = 0 + 1dxy + -1dx2 + -1dx2y
-1dx + dy2X = 1dxy + -1dx2 + -1dx2y

Add '-1dxy' to each side of the equation.
-1dx + -1dxy + dy2X = 1dxy + -1dx2 + -1dxy + -1dx2y

Reorder the terms:
-1dx + -1dxy + dy2X = 1dxy + -1dxy + -1dx2 + -1dx2y

Combine like terms: 1dxy + -1dxy = 0
-1dx + -1dxy + dy2X = 0 + -1dx2 + -1dx2y
-1dx + -1dxy + dy2X = -1dx2 + -1dx2y

Add 'dx2' to each side of the equation.
-1dx + -1dxy + dx2 + dy2X = -1dx2 + dx2 + -1dx2y

Combine like terms: -1dx2 + dx2 = 0
-1dx + -1dxy + dx2 + dy2X = 0 + -1dx2y
-1dx + -1dxy + dx2 + dy2X = -1dx2y

Add 'dx2y' to each side of the equation.
-1dx + -1dxy + dx2 + dx2y + dy2X = -1dx2y + dx2y

Combine like terms: -1dx2y + dx2y = 0
-1dx + -1dxy + dx2 + dx2y + dy2X = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1x + -1xy + x2 + x2y + y2X) = 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 + -1xy + x2 + x2y + y2X)' equal to zero and attempt to solve:

Simplifying
-1x + -1xy + x2 + x2y + y2X = 0

Solving
-1x + -1xy + x2 + x2y + y2X = 0

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

Add 'x' to each side of the equation.
-1x + -1xy + x2 + x2y + x + y2X = 0 + x

Reorder the terms:
-1x + x + -1xy + x2 + x2y + y2X = 0 + x

Combine like terms: -1x + x = 0
0 + -1xy + x2 + x2y + y2X = 0 + x
-1xy + x2 + x2y + y2X = 0 + x
Remove the zero:
-1xy + x2 + x2y + y2X = x

Add 'xy' to each side of the equation.
-1xy + x2 + x2y + xy + y2X = x + xy

Reorder the terms:
-1xy + xy + x2 + x2y + y2X = x + xy

Combine like terms: -1xy + xy = 0
0 + x2 + x2y + y2X = x + xy
x2 + x2y + y2X = x + xy

Add '-1x2' to each side of the equation.
x2 + x2y + -1x2 + y2X = x + xy + -1x2

Reorder the terms:
x2 + -1x2 + x2y + y2X = x + xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + x2y + y2X = x + xy + -1x2
x2y + y2X = x + xy + -1x2

Add '-1x2y' to each side of the equation.
x2y + -1x2y + y2X = x + xy + -1x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + y2X = x + xy + -1x2 + -1x2y
y2X = x + xy + -1x2 + -1x2y

Add '-1y2X' to each side of the equation.
y2X + -1y2X = x + xy + -1x2 + -1x2y + -1y2X

Combine like terms: y2X + -1y2X = 0
0 = x + xy + -1x2 + -1x2y + -1y2X

Simplifying
0 = x + xy + -1x2 + -1x2y + -1y2X

The solution to this equation could not be determined.

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