(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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