(x-y)dx+sdy=0

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


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

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

Reorder the terms:
(-1dxy + dx2) + sdy = 0
(-1dxy + dx2) + sdy = 0

Reorder the terms:
dsy + -1dxy + dx2 = 0

Solving
dsy + -1dxy + dx2 = 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(sy + -1xy + x2) = 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 '(sy + -1xy + x2)' equal to zero and attempt to solve:

Simplifying
sy + -1xy + x2 = 0

Solving
sy + -1xy + x2 = 0

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

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

Reorder the terms:
sy + -1sy + -1xy + x2 = 0 + -1sy

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

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

Combine like terms: -1xy + xy = 0
0 + x2 = -1sy + xy
x2 = -1sy + xy

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

Combine like terms: x2 + -1x2 = 0
0 = -1sy + xy + -1x2

Simplifying
0 = -1sy + xy + -1x2

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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