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Simplifying (1 + -1x) * dy = x(y + 1) * dx Reorder the terms for easier multiplication: dy(1 + -1x) = x(y + 1) * dx (1 * dy + -1x * dy) = x(y + 1) * dx Reorder the terms: (-1dxy + 1dy) = x(y + 1) * dx (-1dxy + 1dy) = x(y + 1) * dx Reorder the terms: -1dxy + 1dy = x(1 + y) * dx Reorder the terms for easier multiplication: -1dxy + 1dy = x * dx(1 + y) Multiply x * dx -1dxy + 1dy = dx2(1 + y) -1dxy + 1dy = (1 * dx2 + y * dx2) -1dxy + 1dy = (1dx2 + dx2y) Solving -1dxy + 1dy = 1dx2 + dx2y Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx2' to each side of the equation. -1dxy + -1dx2 + 1dy = 1dx2 + -1dx2 + dx2y Combine like terms: 1dx2 + -1dx2 = 0 -1dxy + -1dx2 + 1dy = 0 + dx2y -1dxy + -1dx2 + 1dy = dx2y Add '-1dx2y' to each side of the equation. -1dxy + -1dx2 + -1dx2y + 1dy = dx2y + -1dx2y Combine like terms: dx2y + -1dx2y = 0 -1dxy + -1dx2 + -1dx2y + 1dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1xy + -1x2 + -1x2y + y) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(-1xy + -1x2 + -1x2y + y)' equal to zero and attempt to solve: Simplifying -1xy + -1x2 + -1x2y + y = 0 Solving -1xy + -1x2 + -1x2y + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'xy' to each side of the equation. -1xy + -1x2 + -1x2y + xy + y = 0 + xy Reorder the terms: -1xy + xy + -1x2 + -1x2y + y = 0 + xy Combine like terms: -1xy + xy = 0 0 + -1x2 + -1x2y + y = 0 + xy -1x2 + -1x2y + y = 0 + xy Remove the zero: -1x2 + -1x2y + y = xy Add 'x2' to each side of the equation. -1x2 + -1x2y + x2 + y = xy + x2 Reorder the terms: -1x2 + x2 + -1x2y + y = xy + x2 Combine like terms: -1x2 + x2 = 0 0 + -1x2y + y = xy + x2 -1x2y + y = xy + x2 Add 'x2y' to each side of the equation. -1x2y + x2y + y = xy + x2 + x2y Combine like terms: -1x2y + x2y = 0 0 + y = xy + x2 + x2y y = xy + x2 + x2y Add '-1y' to each side of the equation. y + -1y = xy + x2 + x2y + -1y Combine like terms: y + -1y = 0 0 = xy + x2 + x2y + -1y Simplifying 0 = xy + x2 + x2y + -1y 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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