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

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


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

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

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

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

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

Reorder the terms:
4dx + dxy + (dxy + -5dy) = 0
4dx + dxy + (dxy + -5dy) = 0

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

Solving
4dx + 2dxy + -5dy = 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 + 2xy + -5y) = 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 + 2xy + -5y)' equal to zero and attempt to solve: Simplifying 4x + 2xy + -5y = 0 Solving 4x + 2xy + -5y = 0 Move all terms containing d to the left, all other terms to the right. Add '-4x' to each side of the equation. 4x + 2xy + -4x + -5y = 0 + -4x Reorder the terms: 4x + -4x + 2xy + -5y = 0 + -4x Combine like terms: 4x + -4x = 0 0 + 2xy + -5y = 0 + -4x 2xy + -5y = 0 + -4x Remove the zero: 2xy + -5y = -4x Add '-2xy' to each side of the equation. 2xy + -2xy + -5y = -4x + -2xy Combine like terms: 2xy + -2xy = 0 0 + -5y = -4x + -2xy -5y = -4x + -2xy Add '5y' to each side of the equation. -5y + 5y = -4x + -2xy + 5y Combine like terms: -5y + 5y = 0 0 = -4x + -2xy + 5y Simplifying 0 = -4x + -2xy + 5y 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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