2(x-y)dx+dy=0

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

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

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

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

Solving
-2dxy + 2dx2 + dy = 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(-2xy + 2x2 + 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 '(-2xy + 2x2 + y)' equal to zero and attempt to solve:

Simplifying
-2xy + 2x2 + y = 0

Solving
-2xy + 2x2 + y = 0

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

Add '2xy' to each side of the equation.
-2xy + 2x2 + 2xy + y = 0 + 2xy

Reorder the terms:
-2xy + 2xy + 2x2 + y = 0 + 2xy

Combine like terms: -2xy + 2xy = 0
0 + 2x2 + y = 0 + 2xy
2x2 + y = 0 + 2xy
Remove the zero:
2x2 + y = 2xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 + y = 2xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + y = 2xy + -2x2
y = 2xy + -2x2

Add '-1y' to each side of the equation.
y + -1y = 2xy + -2x2 + -1y

Combine like terms: y + -1y = 0
0 = 2xy + -2x2 + -1y

Simplifying
0 = 2xy + -2x2 + -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}