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

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


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

Reorder the terms:
(4 + 4X + -3y) * dy + (3y + -4x) * dx = 0

Reorder the terms for easier multiplication:
dy(4 + 4X + -3y) + (3y + -4x) * dx = 0
(4 * dy + 4X * dy + -3y * dy) + (3y + -4x) * dx = 0
(4dy + 4dyX + -3dy2) + (3y + -4x) * dx = 0

Reorder the terms:
4dy + 4dyX + -3dy2 + (-4x + 3y) * dx = 0

Reorder the terms for easier multiplication:
4dy + 4dyX + -3dy2 + dx(-4x + 3y) = 0
4dy + 4dyX + -3dy2 + (-4x * dx + 3y * dx) = 0

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

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

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