(2x-3y-1)dx+(4x+6y-5)dy=0

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Solution for (2x-3y-1)dx+(4x+6y-5)dy=0 equation:


Simplifying
(2x + -3y + -1) * dx + (4x + 6y + -5) * dy = 0

Reorder the terms:
(-1 + 2x + -3y) * dx + (4x + 6y + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 2x + -3y) + (4x + 6y + -5) * dy = 0
(-1 * dx + 2x * dx + -3y * dx) + (4x + 6y + -5) * dy = 0

Reorder the terms:
(-1dx + -3dxy + 2dx2) + (4x + 6y + -5) * dy = 0
(-1dx + -3dxy + 2dx2) + (4x + 6y + -5) * dy = 0

Reorder the terms:
-1dx + -3dxy + 2dx2 + (-5 + 4x + 6y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + -3dxy + 2dx2 + dy(-5 + 4x + 6y) = 0
-1dx + -3dxy + 2dx2 + (-5 * dy + 4x * dy + 6y * dy) = 0

Reorder the terms:
-1dx + -3dxy + 2dx2 + (4dxy + -5dy + 6dy2) = 0
-1dx + -3dxy + 2dx2 + (4dxy + -5dy + 6dy2) = 0

Reorder the terms:
-1dx + -3dxy + 4dxy + 2dx2 + -5dy + 6dy2 = 0

Combine like terms: -3dxy + 4dxy = 1dxy
-1dx + 1dxy + 2dx2 + -5dy + 6dy2 = 0

Solving
-1dx + 1dxy + 2dx2 + -5dy + 6dy2 = 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 + xy + 2x2 + -5y + 6y2) = 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 + xy + 2x2 + -5y + 6y2)' equal to zero and attempt to solve: Simplifying -1x + xy + 2x2 + -5y + 6y2 = 0 Solving -1x + xy + 2x2 + -5y + 6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + xy + 2x2 + -5y + x + 6y2 = 0 + x Reorder the terms: -1x + x + xy + 2x2 + -5y + 6y2 = 0 + x Combine like terms: -1x + x = 0 0 + xy + 2x2 + -5y + 6y2 = 0 + x xy + 2x2 + -5y + 6y2 = 0 + x Remove the zero: xy + 2x2 + -5y + 6y2 = x Add '-1xy' to each side of the equation. xy + 2x2 + -5y + -1xy + 6y2 = x + -1xy Reorder the terms: xy + -1xy + 2x2 + -5y + 6y2 = x + -1xy Combine like terms: xy + -1xy = 0 0 + 2x2 + -5y + 6y2 = x + -1xy 2x2 + -5y + 6y2 = x + -1xy Add '-2x2' to each side of the equation. 2x2 + -5y + -2x2 + 6y2 = x + -1xy + -2x2 Reorder the terms: 2x2 + -2x2 + -5y + 6y2 = x + -1xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -5y + 6y2 = x + -1xy + -2x2 -5y + 6y2 = x + -1xy + -2x2 Add '5y' to each side of the equation. -5y + 5y + 6y2 = x + -1xy + -2x2 + 5y Combine like terms: -5y + 5y = 0 0 + 6y2 = x + -1xy + -2x2 + 5y 6y2 = x + -1xy + -2x2 + 5y Add '-6y2' to each side of the equation. 6y2 + -6y2 = x + -1xy + -2x2 + 5y + -6y2 Combine like terms: 6y2 + -6y2 = 0 0 = x + -1xy + -2x2 + 5y + -6y2 Simplifying 0 = x + -1xy + -2x2 + 5y + -6y2 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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