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

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


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

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

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

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

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

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

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

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

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

Solving
-1dx + -1dxy + 2dx2 + -4dy = 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 + -1xy + 2x2 + -4y) = 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 + -1xy + 2x2 + -4y)' equal to zero and attempt to solve: Simplifying -1x + -1xy + 2x2 + -4y = 0 Solving -1x + -1xy + 2x2 + -4y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -1xy + 2x2 + x + -4y = 0 + x Reorder the terms: -1x + x + -1xy + 2x2 + -4y = 0 + x Combine like terms: -1x + x = 0 0 + -1xy + 2x2 + -4y = 0 + x -1xy + 2x2 + -4y = 0 + x Remove the zero: -1xy + 2x2 + -4y = x Add 'xy' to each side of the equation. -1xy + 2x2 + xy + -4y = x + xy Reorder the terms: -1xy + xy + 2x2 + -4y = x + xy Combine like terms: -1xy + xy = 0 0 + 2x2 + -4y = x + xy 2x2 + -4y = x + xy Add '-2x2' to each side of the equation. 2x2 + -2x2 + -4y = x + xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -4y = x + xy + -2x2 -4y = x + xy + -2x2 Add '4y' to each side of the equation. -4y + 4y = x + xy + -2x2 + 4y Combine like terms: -4y + 4y = 0 0 = x + xy + -2x2 + 4y Simplifying 0 = x + xy + -2x2 + 4y 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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