(x+2y-4)dx-(2x+y-5)dy=0

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Solution for (x+2y-4)dx-(2x+y-5)dy=0 equation:


Simplifying
(x + 2y + -4) * dx + -1(2x + y + -5) * dy = 0

Reorder the terms:
(-4 + x + 2y) * dx + -1(2x + y + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(-4 + x + 2y) + -1(2x + y + -5) * dy = 0
(-4 * dx + x * dx + 2y * dx) + -1(2x + y + -5) * dy = 0

Reorder the terms:
(-4dx + 2dxy + dx2) + -1(2x + y + -5) * dy = 0
(-4dx + 2dxy + dx2) + -1(2x + y + -5) * dy = 0

Reorder the terms:
-4dx + 2dxy + dx2 + -1(-5 + 2x + y) * dy = 0

Reorder the terms for easier multiplication:
-4dx + 2dxy + dx2 + -1dy(-5 + 2x + y) = 0
-4dx + 2dxy + dx2 + (-5 * -1dy + 2x * -1dy + y * -1dy) = 0

Reorder the terms:
-4dx + 2dxy + dx2 + (-2dxy + 5dy + -1dy2) = 0
-4dx + 2dxy + dx2 + (-2dxy + 5dy + -1dy2) = 0

Reorder the terms:
-4dx + 2dxy + -2dxy + dx2 + 5dy + -1dy2 = 0

Combine like terms: 2dxy + -2dxy = 0
-4dx + 0 + dx2 + 5dy + -1dy2 = 0
-4dx + dx2 + 5dy + -1dy2 = 0

Solving
-4dx + dx2 + 5dy + -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(-4x + x2 + 5y + -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 '(-4x + x2 + 5y + -1y2)' equal to zero and attempt to solve: Simplifying -4x + x2 + 5y + -1y2 = 0 Solving -4x + x2 + 5y + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '4x' to each side of the equation. -4x + x2 + 5y + 4x + -1y2 = 0 + 4x Reorder the terms: -4x + 4x + x2 + 5y + -1y2 = 0 + 4x Combine like terms: -4x + 4x = 0 0 + x2 + 5y + -1y2 = 0 + 4x x2 + 5y + -1y2 = 0 + 4x Remove the zero: x2 + 5y + -1y2 = 4x Add '-1x2' to each side of the equation. x2 + 5y + -1x2 + -1y2 = 4x + -1x2 Reorder the terms: x2 + -1x2 + 5y + -1y2 = 4x + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 5y + -1y2 = 4x + -1x2 5y + -1y2 = 4x + -1x2 Add '-5y' to each side of the equation. 5y + -5y + -1y2 = 4x + -1x2 + -5y Combine like terms: 5y + -5y = 0 0 + -1y2 = 4x + -1x2 + -5y -1y2 = 4x + -1x2 + -5y Add 'y2' to each side of the equation. -1y2 + y2 = 4x + -1x2 + -5y + y2 Combine like terms: -1y2 + y2 = 0 0 = 4x + -1x2 + -5y + y2 Simplifying 0 = 4x + -1x2 + -5y + 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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