(2x+y-1)dx-(4x+2y-4)dy=0

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Solution for (2x+y-1)dx-(4x+2y-4)dy=0 equation:


Simplifying
(2x + y + -1) * dx + -1(4x + 2y + -4) * dy = 0

Reorder the terms:
(-1 + 2x + y) * dx + -1(4x + 2y + -4) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 2x + y) + -1(4x + 2y + -4) * dy = 0
(-1 * dx + 2x * dx + y * dx) + -1(4x + 2y + -4) * dy = 0

Reorder the terms:
(-1dx + dxy + 2dx2) + -1(4x + 2y + -4) * dy = 0
(-1dx + dxy + 2dx2) + -1(4x + 2y + -4) * dy = 0

Reorder the terms:
-1dx + dxy + 2dx2 + -1(-4 + 4x + 2y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + dxy + 2dx2 + -1dy(-4 + 4x + 2y) = 0
-1dx + dxy + 2dx2 + (-4 * -1dy + 4x * -1dy + 2y * -1dy) = 0

Reorder the terms:
-1dx + dxy + 2dx2 + (-4dxy + 4dy + -2dy2) = 0
-1dx + dxy + 2dx2 + (-4dxy + 4dy + -2dy2) = 0

Reorder the terms:
-1dx + dxy + -4dxy + 2dx2 + 4dy + -2dy2 = 0

Combine like terms: dxy + -4dxy = -3dxy
-1dx + -3dxy + 2dx2 + 4dy + -2dy2 = 0

Solving
-1dx + -3dxy + 2dx2 + 4dy + -2dy2 = 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(-1x + -3xy + 2x2 + 4y + -2y2) = 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 '(-1x + -3xy + 2x2 + 4y + -2y2)' equal to zero and attempt to solve: Simplifying -1x + -3xy + 2x2 + 4y + -2y2 = 0 Solving -1x + -3xy + 2x2 + 4y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -3xy + 2x2 + 4y + x + -2y2 = 0 + x Reorder the terms: -1x + x + -3xy + 2x2 + 4y + -2y2 = 0 + x Combine like terms: -1x + x = 0 0 + -3xy + 2x2 + 4y + -2y2 = 0 + x -3xy + 2x2 + 4y + -2y2 = 0 + x Remove the zero: -3xy + 2x2 + 4y + -2y2 = x Add '3xy' to each side of the equation. -3xy + 2x2 + 4y + 3xy + -2y2 = x + 3xy Reorder the terms: -3xy + 3xy + 2x2 + 4y + -2y2 = x + 3xy Combine like terms: -3xy + 3xy = 0 0 + 2x2 + 4y + -2y2 = x + 3xy 2x2 + 4y + -2y2 = x + 3xy Add '-2x2' to each side of the equation. 2x2 + 4y + -2x2 + -2y2 = x + 3xy + -2x2 Reorder the terms: 2x2 + -2x2 + 4y + -2y2 = x + 3xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 4y + -2y2 = x + 3xy + -2x2 4y + -2y2 = x + 3xy + -2x2 Add '-4y' to each side of the equation. 4y + -4y + -2y2 = x + 3xy + -2x2 + -4y Combine like terms: 4y + -4y = 0 0 + -2y2 = x + 3xy + -2x2 + -4y -2y2 = x + 3xy + -2x2 + -4y Add '2y2' to each side of the equation. -2y2 + 2y2 = x + 3xy + -2x2 + -4y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = x + 3xy + -2x2 + -4y + 2y2 Simplifying 0 = x + 3xy + -2x2 + -4y + 2y2 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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