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

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


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

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

Reorder the terms:
(dxy + dx2) + (x + y + -4) * dy = 0
(dxy + dx2) + (x + y + -4) * dy = 0

Reorder the terms:
dxy + dx2 + (-4 + x + y) * dy = 0

Reorder the terms for easier multiplication:
dxy + dx2 + dy(-4 + x + y) = 0
dxy + dx2 + (-4 * dy + x * dy + y * dy) = 0

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

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

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

Solving
2dxy + dx2 + -4dy + dy2 = 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(2xy + x2 + -4y + y2) = 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 '(2xy + x2 + -4y + y2)' equal to zero and attempt to solve: Simplifying 2xy + x2 + -4y + y2 = 0 Solving 2xy + x2 + -4y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy' to each side of the equation. 2xy + x2 + -4y + -2xy + y2 = 0 + -2xy Reorder the terms: 2xy + -2xy + x2 + -4y + y2 = 0 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + -4y + y2 = 0 + -2xy x2 + -4y + y2 = 0 + -2xy Remove the zero: x2 + -4y + y2 = -2xy Add '-1x2' to each side of the equation. x2 + -4y + -1x2 + y2 = -2xy + -1x2 Reorder the terms: x2 + -1x2 + -4y + y2 = -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -4y + y2 = -2xy + -1x2 -4y + y2 = -2xy + -1x2 Add '4y' to each side of the equation. -4y + 4y + y2 = -2xy + -1x2 + 4y Combine like terms: -4y + 4y = 0 0 + y2 = -2xy + -1x2 + 4y y2 = -2xy + -1x2 + 4y Add '-1y2' to each side of the equation. y2 + -1y2 = -2xy + -1x2 + 4y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -2xy + -1x2 + 4y + -1y2 Simplifying 0 = -2xy + -1x2 + 4y + -1y2 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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