(y+2)dx+(x-2)dy=0

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Solution for (y+2)dx+(x-2)dy=0 equation: 


Simplifying
(y + 2) * dx + (x + -2) * dy = 0

Reorder the terms:
(2 + y) * dx + (x + -2) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + y) + (x + -2) * dy = 0
(2 * dx + y * dx) + (x + -2) * dy = 0
(2dx + dxy) + (x + -2) * dy = 0

Reorder the terms:
2dx + dxy + (-2 + x) * dy = 0

Reorder the terms for easier multiplication:
2dx + dxy + dy(-2 + x) = 0
2dx + dxy + (-2 * dy + x * dy) = 0

Reorder the terms:
2dx + dxy + (dxy + -2dy) = 0
2dx + dxy + (dxy + -2dy) = 0

Combine like terms: dxy + dxy = 2dxy
2dx + 2dxy + -2dy = 0

Solving
2dx + 2dxy + -2dy = 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), '2d'.
2d(x + xy + -1y) = 0

Ignore the factor 2.

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 + -1y)' equal to zero and attempt to solve:

Simplifying
x + xy + -1y = 0

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

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

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

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

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

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

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

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

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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