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

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


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

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

Reorder the terms for easier multiplication:
dx(-1x + xy) + (xy + y) * dy = 0
(-1x * dx + xy * dx) + (xy + y) * dy = 0
(-1dx2 + dx2y) + (xy + y) * dy = 0

Reorder the terms for easier multiplication:
-1dx2 + dx2y + dy(xy + y) = 0
-1dx2 + dx2y + (xy * dy + y * dy) = 0
-1dx2 + dx2y + (dxy2 + dy2) = 0

Reorder the terms:
dxy2 + -1dx2 + dx2y + dy2 = 0

Solving
dxy2 + -1dx2 + dx2y + dy2 = 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(xy2 + -1x2 + x2y + y2) = 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 '(xy2 + -1x2 + x2y + y2)' equal to zero and attempt to solve:

Simplifying
xy2 + -1x2 + x2y + y2 = 0

Solving
xy2 + -1x2 + x2y + y2 = 0

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

Add '-1xy2' to each side of the equation.
xy2 + -1x2 + x2y + -1xy2 + y2 = 0 + -1xy2

Reorder the terms:
xy2 + -1xy2 + -1x2 + x2y + y2 = 0 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + -1x2 + x2y + y2 = 0 + -1xy2
-1x2 + x2y + y2 = 0 + -1xy2
Remove the zero:
-1x2 + x2y + y2 = -1xy2

Add 'x2' to each side of the equation.
-1x2 + x2y + x2 + y2 = -1xy2 + x2

Reorder the terms:
-1x2 + x2 + x2y + y2 = -1xy2 + x2

Combine like terms: -1x2 + x2 = 0
0 + x2y + y2 = -1xy2 + x2
x2y + y2 = -1xy2 + x2

Add '-1x2y' to each side of the equation.
x2y + -1x2y + y2 = -1xy2 + x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + y2 = -1xy2 + x2 + -1x2y
y2 = -1xy2 + x2 + -1x2y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1xy2 + x2 + -1x2y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1xy2 + x2 + -1x2y + -1y2

Simplifying
0 = -1xy2 + x2 + -1x2y + -1y2

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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