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

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


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

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

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

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

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

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