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

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


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

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

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

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

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

Reorder the terms for easier multiplication:
2dxy + 4dy + -1dy2 + dx(5 + x + -2y) = 0
2dxy + 4dy + -1dy2 + (5 * dx + x * dx + -2y * dx) = 0

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

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

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

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