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

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


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

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

Reorder the terms for easier multiplication:
dx(1 + xy) + (1 + -1x * y)(dy) = 0
(1 * dx + xy * dx) + (1 + -1x * y)(dy) = 0
(1dx + dx2y) + (1 + -1x * y)(dy) = 0

Multiply x * y
1dx + dx2y + (1 + -1xy)(dy) = 0

Reorder the terms for easier multiplication:
1dx + dx2y + dy(1 + -1xy) = 0
1dx + dx2y + (1 * dy + -1xy * dy) = 0

Reorder the terms:
1dx + dx2y + (-1dxy2 + 1dy) = 0
1dx + dx2y + (-1dxy2 + 1dy) = 0

Reorder the terms:
1dx + -1dxy2 + dx2y + 1dy = 0

Solving
1dx + -1dxy2 + dx2y + 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 + -1xy2 + x2y + 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 + -1xy2 + x2y + y)' equal to zero and attempt to solve:

Simplifying
x + -1xy2 + x2y + y = 0

Solving
x + -1xy2 + x2y + 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 + -1xy2 + x2y + -1x + y = 0 + -1x

Reorder the terms:
x + -1x + -1xy2 + x2y + y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -1xy2 + x2y + y = 0 + -1x
-1xy2 + x2y + y = 0 + -1x
Remove the zero:
-1xy2 + x2y + y = -1x

Add 'xy2' to each side of the equation.
-1xy2 + x2y + xy2 + y = -1x + xy2

Reorder the terms:
-1xy2 + xy2 + x2y + y = -1x + xy2

Combine like terms: -1xy2 + xy2 = 0
0 + x2y + y = -1x + xy2
x2y + y = -1x + xy2

Add '-1x2y' to each side of the equation.
x2y + -1x2y + y = -1x + xy2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + y = -1x + xy2 + -1x2y
y = -1x + xy2 + -1x2y

Add '-1y' to each side of the equation.
y + -1y = -1x + xy2 + -1x2y + -1y

Combine like terms: y + -1y = 0
0 = -1x + xy2 + -1x2y + -1y

Simplifying
0 = -1x + xy2 + -1x2y + -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}

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