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

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


Simplifying
(x + y) * dx + -1(x + -1y + -2) * dy = 0

Reorder the terms for easier multiplication:
dx(x + y) + -1(x + -1y + -2) * dy = 0
(x * dx + y * dx) + -1(x + -1y + -2) * dy = 0

Reorder the terms:
(dxy + dx2) + -1(x + -1y + -2) * dy = 0
(dxy + dx2) + -1(x + -1y + -2) * dy = 0

Reorder the terms:
dxy + dx2 + -1(-2 + x + -1y) * dy = 0

Reorder the terms for easier multiplication:
dxy + dx2 + -1dy(-2 + x + -1y) = 0
dxy + dx2 + (-2 * -1dy + x * -1dy + -1y * -1dy) = 0

Reorder the terms:
dxy + dx2 + (-1dxy + 2dy + 1dy2) = 0
dxy + dx2 + (-1dxy + 2dy + 1dy2) = 0

Reorder the terms:
dxy + -1dxy + dx2 + 2dy + 1dy2 = 0

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

Solving
dx2 + 2dy + 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(x2 + 2y + y2) = 0

Factor a trinomial.
d((x + y)(x + y)) = 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 '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1x' to each side of the equation.
x + -1x + y = 0 + -1x

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

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

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

Simplifying
0 = -1x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1x' to each side of the equation.
x + -1x + y = 0 + -1x

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

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

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

Simplifying
0 = -1x + -1y

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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