(X+Y)*dX-(X-1Y)*dY=0

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Solution for (X+Y)*dX-(X-1Y)*dY=0 equation: 


Simplifying
(X + Y) * dX + -1(X + -1Y) * dY = 0

Reorder the terms for easier multiplication:
dX(X + Y) + -1(X + -1Y) * dY = 0
(X * dX + Y * dX) + -1(X + -1Y) * dY = 0

Reorder the terms:
(dXY + dX2) + -1(X + -1Y) * dY = 0
(dXY + dX2) + -1(X + -1Y) * dY = 0

Reorder the terms for easier multiplication:
dXY + dX2 + -1dY(X + -1Y) = 0
dXY + dX2 + (X * -1dY + -1Y * -1dY) = 0
dXY + dX2 + (-1dXY + 1dY2) = 0

Reorder the terms:
dXY + -1dXY + dX2 + 1dY2 = 0

Combine like terms: dXY + -1dXY = 0
0 + dX2 + 1dY2 = 0
dX2 + 1dY2 = 0

Solving
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(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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