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

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


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

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

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

Reorder the terms:
dxy + dy2 = (-1dxy + dx2)
dxy + dy2 = (-1dxy + dx2)

Solving
dxy + dy2 = -1dxy + dx2

Solving for variable 'd'.

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

Add 'dxy' to each side of the equation.
dxy + dxy + dy2 = -1dxy + dxy + dx2

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

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

Add '-1dx2' to each side of the equation.
2dxy + -1dx2 + dy2 = dx2 + -1dx2

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(2xy + -1x2 + 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 '(2xy + -1x2 + y2)' equal to zero and attempt to solve:

Simplifying
2xy + -1x2 + y2 = 0

Solving
2xy + -1x2 + y2 = 0

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

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

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

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

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

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

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

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

Simplifying
0 = -2xy + x2 + -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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