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

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


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

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

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

Remove parenthesis around (2x)
-1dxy + dx2 + -1 * 2x * dy = 0

Multiply -1 * 2
-1dxy + dx2 + -2x * dy = 0

Multiply x * dy
-1dxy + dx2 + -2dxy = 0

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

Combine like terms: -1dxy + -2dxy = -3dxy
-3dxy + dx2 = 0

Solving
-3dxy + 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), 'dx'.
dx(-3y + x) = 0


Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve:

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(-3y + x)' equal to zero and attempt to solve:

Simplifying
-3y + x = 0

Reorder the terms:
x + -3y = 0

Solving
x + -3y = 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 + -3y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -3y = 0 + -1x
-3y = 0 + -1x
Remove the zero:
-3y = -1x

Add '3y' to each side of the equation.
-3y + 3y = -1x + 3y

Combine like terms: -3y + 3y = 0
0 = -1x + 3y

Simplifying
0 = -1x + 3y

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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