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

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


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

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

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

Reorder the terms:
(dxyX + dx2) + (xy + y) * dy = 0
(dxyX + dx2) + (xy + y) * dy = 0

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

Reorder the terms:
dxyX + dxy2 + dx2 + dy2 = 0

Solving
dxyX + dxy2 + dx2 + 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(xyX + xy2 + x2 + 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 '(xyX + xy2 + x2 + y2)' equal to zero and attempt to solve:

Simplifying
xyX + xy2 + x2 + y2 = 0

Solving
xyX + xy2 + x2 + y2 = 0

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -1xyX + -1xy2 + -1x2 + -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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