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Simplifying (1 + x2 + y2 + x2y2) * dy = (1 + y2) * dx Reorder the terms: (1 + x2 + x2y2 + y2) * dy = (1 + y2) * dx Reorder the terms for easier multiplication: dy(1 + x2 + x2y2 + y2) = (1 + y2) * dx (1 * dy + x2 * dy + x2y2 * dy + y2 * dy) = (1 + y2) * dx Reorder the terms: (dx2y + dx2y3 + 1dy + dy3) = (1 + y2) * dx (dx2y + dx2y3 + 1dy + dy3) = (1 + y2) * dx Reorder the terms for easier multiplication: dx2y + dx2y3 + 1dy + dy3 = dx(1 + y2) dx2y + dx2y3 + 1dy + dy3 = (1 * dx + y2 * dx) dx2y + dx2y3 + 1dy + dy3 = (1dx + dxy2) Solving dx2y + dx2y3 + 1dy + dy3 = 1dx + dxy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. dx2y + dx2y3 + 1dy + -1dx + dy3 = 1dx + -1dx + dxy2 Reorder the terms: -1dx + dx2y + dx2y3 + 1dy + dy3 = 1dx + -1dx + dxy2 Combine like terms: 1dx + -1dx = 0 -1dx + dx2y + dx2y3 + 1dy + dy3 = 0 + dxy2 -1dx + dx2y + dx2y3 + 1dy + dy3 = dxy2 Add '-1dxy2' to each side of the equation. -1dx + dx2y + dx2y3 + 1dy + -1dxy2 + dy3 = dxy2 + -1dxy2 Reorder the terms: -1dx + -1dxy2 + dx2y + dx2y3 + 1dy + dy3 = dxy2 + -1dxy2 Combine like terms: dxy2 + -1dxy2 = 0 -1dx + -1dxy2 + dx2y + dx2y3 + 1dy + dy3 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + -1xy2 + x2y + x2y3 + y + y3) = 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 '(-1x + -1xy2 + x2y + x2y3 + y + y3)' equal to zero and attempt to solve: Simplifying -1x + -1xy2 + x2y + x2y3 + y + y3 = 0 Solving -1x + -1xy2 + x2y + x2y3 + y + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -1xy2 + x2y + x2y3 + y + x + y3 = 0 + x Reorder the terms: -1x + x + -1xy2 + x2y + x2y3 + y + y3 = 0 + x Combine like terms: -1x + x = 0 0 + -1xy2 + x2y + x2y3 + y + y3 = 0 + x -1xy2 + x2y + x2y3 + y + y3 = 0 + x Remove the zero: -1xy2 + x2y + x2y3 + y + y3 = x Add 'xy2' to each side of the equation. -1xy2 + x2y + x2y3 + y + xy2 + y3 = x + xy2 Reorder the terms: -1xy2 + xy2 + x2y + x2y3 + y + y3 = x + xy2 Combine like terms: -1xy2 + xy2 = 0 0 + x2y + x2y3 + y + y3 = x + xy2 x2y + x2y3 + y + y3 = x + xy2 Add '-1x2y' to each side of the equation. x2y + x2y3 + y + -1x2y + y3 = x + xy2 + -1x2y Reorder the terms: x2y + -1x2y + x2y3 + y + y3 = x + xy2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + x2y3 + y + y3 = x + xy2 + -1x2y x2y3 + y + y3 = x + xy2 + -1x2y Add '-1x2y3' to each side of the equation. x2y3 + y + -1x2y3 + y3 = x + xy2 + -1x2y + -1x2y3 Reorder the terms: x2y3 + -1x2y3 + y + y3 = x + xy2 + -1x2y + -1x2y3 Combine like terms: x2y3 + -1x2y3 = 0 0 + y + y3 = x + xy2 + -1x2y + -1x2y3 y + y3 = x + xy2 + -1x2y + -1x2y3 Add '-1y' to each side of the equation. y + -1y + y3 = x + xy2 + -1x2y + -1x2y3 + -1y Combine like terms: y + -1y = 0 0 + y3 = x + xy2 + -1x2y + -1x2y3 + -1y y3 = x + xy2 + -1x2y + -1x2y3 + -1y Add '-1y3' to each side of the equation. y3 + -1y3 = x + xy2 + -1x2y + -1x2y3 + -1y + -1y3 Combine like terms: y3 + -1y3 = 0 0 = x + xy2 + -1x2y + -1x2y3 + -1y + -1y3 Simplifying 0 = x + xy2 + -1x2y + -1x2y3 + -1y + -1y3 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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