(2x-y)dx+(4x+y-3)dy=0

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Solution for (2x-y)dx+(4x+y-3)dy=0 equation:


Simplifying
(2x + -1y) * dx + (4x + y + -3) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + -1y) + (4x + y + -3) * dy = 0
(2x * dx + -1y * dx) + (4x + y + -3) * dy = 0

Reorder the terms:
(-1dxy + 2dx2) + (4x + y + -3) * dy = 0
(-1dxy + 2dx2) + (4x + y + -3) * dy = 0

Reorder the terms:
-1dxy + 2dx2 + (-3 + 4x + y) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + 2dx2 + dy(-3 + 4x + y) = 0
-1dxy + 2dx2 + (-3 * dy + 4x * dy + y * dy) = 0

Reorder the terms:
-1dxy + 2dx2 + (4dxy + -3dy + dy2) = 0
-1dxy + 2dx2 + (4dxy + -3dy + dy2) = 0

Reorder the terms:
-1dxy + 4dxy + 2dx2 + -3dy + dy2 = 0

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

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