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

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


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

Reorder the terms for easier multiplication:
dx(Y + x) + -1(y + -1x) * dy = 0
(Y * dx + x * dx) + -1(y + -1x) * dy = 0
(dxY + dx2) + -1(y + -1x) * dy = 0

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

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

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

Solving
dxY + 1dxy + 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(xY + xy + 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 '(xY + xy + x2 + -1y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

Reorder the terms:
xy + -1xy + x2 + -1y2 = -1xY + -1xy

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

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

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

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

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

Simplifying
0 = -1xY + -1xy + -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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