xdy+(xy+y-1)dx=0

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Solution for xdy+(xy+y-1)dx=0 equation:


Simplifying
xdy + (xy + y + -1) * dx = 0

Reorder the terms:
dxy + (-1 + xy + y) * dx = 0

Reorder the terms for easier multiplication:
dxy + dx(-1 + xy + y) = 0
dxy + (-1 * dx + xy * dx + y * dx) = 0

Reorder the terms:
dxy + (-1dx + dxy + dx2y) = 0
dxy + (-1dx + dxy + dx2y) = 0

Reorder the terms:
-1dx + dxy + dxy + dx2y = 0

Combine like terms: dxy + dxy = 2dxy
-1dx + 2dxy + dx2y = 0

Solving
-1dx + 2dxy + dx2y = 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), 'dx'.
dx(-1 + 2y + xy) = 0

Subproblem 1

Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-1 + 2y + xy)' equal to zero and attempt to solve: Simplifying -1 + 2y + xy = 0 Reorder the terms: -1 + xy + 2y = 0 Solving -1 + xy + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + xy + 1 + 2y = 0 + 1 Reorder the terms: -1 + 1 + xy + 2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + xy + 2y = 0 + 1 xy + 2y = 0 + 1 Combine like terms: 0 + 1 = 1 xy + 2y = 1 Add '-1xy' to each side of the equation. xy + -1xy + 2y = 1 + -1xy Combine like terms: xy + -1xy = 0 0 + 2y = 1 + -1xy 2y = 1 + -1xy Add '-2y' to each side of the equation. 2y + -2y = 1 + -1xy + -2y Combine like terms: 2y + -2y = 0 0 = 1 + -1xy + -2y Simplifying 0 = 1 + -1xy + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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