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

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


Simplifying
(y + -1x * y + x + -1) * dx + x2 * dy = 0

Multiply x * y
(y + -1xy + x + -1) * dx + x2 * dy = 0

Reorder the terms:
(-1 + x + -1xy + y) * dx + x2 * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + x + -1xy + y) + x2 * dy = 0
(-1 * dx + x * dx + -1xy * dx + y * dx) + x2 * dy = 0

Reorder the terms:
(-1dx + dxy + dx2 + -1dx2y) + x2 * dy = 0
(-1dx + dxy + dx2 + -1dx2y) + x2 * dy = 0

Multiply x2 * dy
-1dx + dxy + dx2 + -1dx2y + dx2y = 0

Combine like terms: -1dx2y + dx2y = 0
-1dx + dxy + dx2 + 0 = 0
-1dx + dxy + dx2 = 0

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