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

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


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

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

Reorder the terms:
(-1dxy + dx2) + -1(x + y) * dy = 0
(-1dxy + dx2) + -1(x + y) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + dx2 + -1dy(x + y) = 0
-1dxy + dx2 + (x * -1dy + y * -1dy) = 0
-1dxy + dx2 + (-1dxy + -1dy2) = 0

Reorder the terms:
-1dxy + -1dxy + dx2 + -1dy2 = 0

Combine like terms: -1dxy + -1dxy = -2dxy
-2dxy + dx2 + -1dy2 = 0

Solving
-2dxy + dx2 + -1dy2 = 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(-2xy + x2 + -1y2) = 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 '(-2xy + x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
-2xy + x2 + -1y2 = 0

Solving
-2xy + x2 + -1y2 = 0

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

Add '2xy' to each side of the equation.
-2xy + x2 + 2xy + -1y2 = 0 + 2xy

Reorder the terms:
-2xy + 2xy + x2 + -1y2 = 0 + 2xy

Combine like terms: -2xy + 2xy = 0
0 + x2 + -1y2 = 0 + 2xy
x2 + -1y2 = 0 + 2xy
Remove the zero:
x2 + -1y2 = 2xy

Add '-1x2' to each side of the equation.
x2 + -1x2 + -1y2 = 2xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -1y2 = 2xy + -1x2
-1y2 = 2xy + -1x2

Add 'y2' to each side of the equation.
-1y2 + y2 = 2xy + -1x2 + y2

Combine like terms: -1y2 + y2 = 0
0 = 2xy + -1x2 + y2

Simplifying
0 = 2xy + -1x2 + y2

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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