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

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


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

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

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

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

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

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

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

Solving
dx2 = -1dy2

Solving for variable 'd'.

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

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

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

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

Simplifying
x2 + y2 = 0

Solving
x2 + y2 = 0

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

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

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

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

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

Simplifying
0 = -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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