(y-2)dx+(3x-y)dy=0

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Solution for (y-2)dx+(3x-y)dy=0 equation: 


Simplifying
(y + -2) * dx + (3x + -1y) * dy = 0

Reorder the terms:
(-2 + y) * dx + (3x + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(-2 + y) + (3x + -1y) * dy = 0
(-2 * dx + y * dx) + (3x + -1y) * dy = 0
(-2dx + dxy) + (3x + -1y) * dy = 0

Reorder the terms for easier multiplication:
-2dx + dxy + dy(3x + -1y) = 0
-2dx + dxy + (3x * dy + -1y * dy) = 0
-2dx + dxy + (3dxy + -1dy2) = 0

Combine like terms: dxy + 3dxy = 4dxy
-2dx + 4dxy + -1dy2 = 0

Solving
-2dx + 4dxy + -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(-2x + 4xy + -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 '(-2x + 4xy + -1y2)' equal to zero and attempt to solve:

Simplifying
-2x + 4xy + -1y2 = 0

Solving
-2x + 4xy + -1y2 = 0

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

Add '2x' to each side of the equation.
-2x + 4xy + 2x + -1y2 = 0 + 2x

Reorder the terms:
-2x + 2x + 4xy + -1y2 = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + 4xy + -1y2 = 0 + 2x
4xy + -1y2 = 0 + 2x
Remove the zero:
4xy + -1y2 = 2x

Add '-4xy' to each side of the equation.
4xy + -4xy + -1y2 = 2x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + -1y2 = 2x + -4xy
-1y2 = 2x + -4xy

Add 'y2' to each side of the equation.
-1y2 + y2 = 2x + -4xy + y2

Combine like terms: -1y2 + y2 = 0
0 = 2x + -4xy + y2

Simplifying
0 = 2x + -4xy + 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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