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Simplifying (1 + y2 + xy2) * dx + y(x2y + y + 2xy) * dy = 0 Reorder the terms: (1 + xy2 + y2) * dx + y(x2y + y + 2xy) * dy = 0 Reorder the terms for easier multiplication: dx(1 + xy2 + y2) + y(x2y + y + 2xy) * dy = 0 (1 * dx + xy2 * dx + y2 * dx) + y(x2y + y + 2xy) * dy = 0 Reorder the terms: (1dx + dxy2 + dx2y2) + y(x2y + y + 2xy) * dy = 0 (1dx + dxy2 + dx2y2) + y(x2y + y + 2xy) * dy = 0 Reorder the terms: 1dx + dxy2 + dx2y2 + y(2xy + x2y + y) * dy = 0 Reorder the terms for easier multiplication: 1dx + dxy2 + dx2y2 + y * dy(2xy + x2y + y) = 0 Multiply y * dy 1dx + dxy2 + dx2y2 + dy2(2xy + x2y + y) = 0 1dx + dxy2 + dx2y2 + (2xy * dy2 + x2y * dy2 + y * dy2) = 0 1dx + dxy2 + dx2y2 + (2dxy3 + dx2y3 + dy3) = 0 Reorder the terms: 1dx + dxy2 + 2dxy3 + dx2y2 + dx2y3 + dy3 = 0 Solving 1dx + dxy2 + 2dxy3 + dx2y2 + dx2y3 + dy3 = 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), 'd'. d(x + xy2 + 2xy3 + x2y2 + x2y3 + 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 '(x + xy2 + 2xy3 + x2y2 + x2y3 + y3)' equal to zero and attempt to solve: Simplifying x + xy2 + 2xy3 + x2y2 + x2y3 + y3 = 0 Solving x + xy2 + 2xy3 + x2y2 + x2y3 + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + xy2 + 2xy3 + x2y2 + x2y3 + -1x + y3 = 0 + -1x Reorder the terms: x + -1x + xy2 + 2xy3 + x2y2 + x2y3 + y3 = 0 + -1x Combine like terms: x + -1x = 0 0 + xy2 + 2xy3 + x2y2 + x2y3 + y3 = 0 + -1x xy2 + 2xy3 + x2y2 + x2y3 + y3 = 0 + -1x Remove the zero: xy2 + 2xy3 + x2y2 + x2y3 + y3 = -1x Add '-1xy2' to each side of the equation. xy2 + 2xy3 + x2y2 + x2y3 + -1xy2 + y3 = -1x + -1xy2 Reorder the terms: xy2 + -1xy2 + 2xy3 + x2y2 + x2y3 + y3 = -1x + -1xy2 Combine like terms: xy2 + -1xy2 = 0 0 + 2xy3 + x2y2 + x2y3 + y3 = -1x + -1xy2 2xy3 + x2y2 + x2y3 + y3 = -1x + -1xy2 Add '-2xy3' to each side of the equation. 2xy3 + x2y2 + x2y3 + -2xy3 + y3 = -1x + -1xy2 + -2xy3 Reorder the terms: 2xy3 + -2xy3 + x2y2 + x2y3 + y3 = -1x + -1xy2 + -2xy3 Combine like terms: 2xy3 + -2xy3 = 0 0 + x2y2 + x2y3 + y3 = -1x + -1xy2 + -2xy3 x2y2 + x2y3 + y3 = -1x + -1xy2 + -2xy3 Add '-1x2y2' to each side of the equation. x2y2 + x2y3 + -1x2y2 + y3 = -1x + -1xy2 + -2xy3 + -1x2y2 Reorder the terms: x2y2 + -1x2y2 + x2y3 + y3 = -1x + -1xy2 + -2xy3 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + x2y3 + y3 = -1x + -1xy2 + -2xy3 + -1x2y2 x2y3 + y3 = -1x + -1xy2 + -2xy3 + -1x2y2 Add '-1x2y3' to each side of the equation. x2y3 + -1x2y3 + y3 = -1x + -1xy2 + -2xy3 + -1x2y2 + -1x2y3 Combine like terms: x2y3 + -1x2y3 = 0 0 + y3 = -1x + -1xy2 + -2xy3 + -1x2y2 + -1x2y3 y3 = -1x + -1xy2 + -2xy3 + -1x2y2 + -1x2y3 Add '-1y3' to each side of the equation. y3 + -1y3 = -1x + -1xy2 + -2xy3 + -1x2y2 + -1x2y3 + -1y3 Combine like terms: y3 + -1y3 = 0 0 = -1x + -1xy2 + -2xy3 + -1x2y2 + -1x2y3 + -1y3 Simplifying 0 = -1x + -1xy2 + -2xy3 + -1x2y2 + -1x2y3 + -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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