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

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


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

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

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

Solving
1dx + dxy + 1dy + -1dyX = 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 + xy + y + -1yX) = 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 + xy + y + -1yX)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

Reorder the terms:
xy + -1xy + y + -1yX = -1x + -1xy

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

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

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

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

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

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

The solution to this equation could not be determined.

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

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