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Simplifying dy = (1 + x + y2 + xy2) * dx Reorder the terms: dy = (1 + x + xy2 + y2) * dx Reorder the terms for easier multiplication: dy = dx(1 + x + xy2 + y2) dy = (1 * dx + x * dx + xy2 * dx + y2 * dx) Reorder the terms: dy = (1dx + dxy2 + dx2 + dx2y2) dy = (1dx + dxy2 + dx2 + dx2y2) Solving dy = 1dx + dxy2 + dx2 + dx2y2 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. -1dx + dy = 1dx + dxy2 + dx2 + -1dx + dx2y2 Reorder the terms: -1dx + dy = 1dx + -1dx + dxy2 + dx2 + dx2y2 Combine like terms: 1dx + -1dx = 0 -1dx + dy = 0 + dxy2 + dx2 + dx2y2 -1dx + dy = dxy2 + dx2 + dx2y2 Add '-1dxy2' to each side of the equation. -1dx + -1dxy2 + dy = dxy2 + dx2 + -1dxy2 + dx2y2 Reorder the terms: -1dx + -1dxy2 + dy = dxy2 + -1dxy2 + dx2 + dx2y2 Combine like terms: dxy2 + -1dxy2 = 0 -1dx + -1dxy2 + dy = 0 + dx2 + dx2y2 -1dx + -1dxy2 + dy = dx2 + dx2y2 Add '-1dx2' to each side of the equation. -1dx + -1dxy2 + -1dx2 + dy = dx2 + -1dx2 + dx2y2 Combine like terms: dx2 + -1dx2 = 0 -1dx + -1dxy2 + -1dx2 + dy = 0 + dx2y2 -1dx + -1dxy2 + -1dx2 + dy = dx2y2 Add '-1dx2y2' to each side of the equation. -1dx + -1dxy2 + -1dx2 + -1dx2y2 + dy = dx2y2 + -1dx2y2 Combine like terms: dx2y2 + -1dx2y2 = 0 -1dx + -1dxy2 + -1dx2 + -1dx2y2 + dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + -1xy2 + -1x2 + -1x2y2 + 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 '(-1x + -1xy2 + -1x2 + -1x2y2 + y)' equal to zero and attempt to solve: Simplifying -1x + -1xy2 + -1x2 + -1x2y2 + y = 0 Solving -1x + -1xy2 + -1x2 + -1x2y2 + y = 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 + -1x2 + -1x2y2 + x + y = 0 + x Reorder the terms: -1x + x + -1xy2 + -1x2 + -1x2y2 + y = 0 + x Combine like terms: -1x + x = 0 0 + -1xy2 + -1x2 + -1x2y2 + y = 0 + x -1xy2 + -1x2 + -1x2y2 + y = 0 + x Remove the zero: -1xy2 + -1x2 + -1x2y2 + y = x Add 'xy2' to each side of the equation. -1xy2 + -1x2 + -1x2y2 + xy2 + y = x + xy2 Reorder the terms: -1xy2 + xy2 + -1x2 + -1x2y2 + y = x + xy2 Combine like terms: -1xy2 + xy2 = 0 0 + -1x2 + -1x2y2 + y = x + xy2 -1x2 + -1x2y2 + y = x + xy2 Add 'x2' to each side of the equation. -1x2 + -1x2y2 + x2 + y = x + xy2 + x2 Reorder the terms: -1x2 + x2 + -1x2y2 + y = x + xy2 + x2 Combine like terms: -1x2 + x2 = 0 0 + -1x2y2 + y = x + xy2 + x2 -1x2y2 + y = x + xy2 + x2 Add 'x2y2' to each side of the equation. -1x2y2 + x2y2 + y = x + xy2 + x2 + x2y2 Combine like terms: -1x2y2 + x2y2 = 0 0 + y = x + xy2 + x2 + x2y2 y = x + xy2 + x2 + x2y2 Add '-1y' to each side of the equation. y + -1y = x + xy2 + x2 + x2y2 + -1y Combine like terms: y + -1y = 0 0 = x + xy2 + x2 + x2y2 + -1y Simplifying 0 = x + xy2 + x2 + x2y2 + -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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