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Simplifying (1 + y2) * dx + -1(y4 + y2 + 2xy) * dy = 0 Reorder the terms for easier multiplication: dx(1 + y2) + -1(y4 + y2 + 2xy) * dy = 0 (1 * dx + y2 * dx) + -1(y4 + y2 + 2xy) * dy = 0 (1dx + dxy2) + -1(y4 + y2 + 2xy) * dy = 0 Reorder the terms: 1dx + dxy2 + -1(2xy + y2 + y4) * dy = 0 Reorder the terms for easier multiplication: 1dx + dxy2 + -1dy(2xy + y2 + y4) = 0 1dx + dxy2 + (2xy * -1dy + y2 * -1dy + y4 * -1dy) = 0 1dx + dxy2 + (-2dxy2 + -1dy3 + -1dy5) = 0 Combine like terms: dxy2 + -2dxy2 = -1dxy2 1dx + -1dxy2 + -1dy3 + -1dy5 = 0 Solving 1dx + -1dxy2 + -1dy3 + -1dy5 = 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 + -1xy2 + -1y3 + -1y5) = 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 + -1xy2 + -1y3 + -1y5)' equal to zero and attempt to solve: Simplifying x + -1xy2 + -1y3 + -1y5 = 0 Solving x + -1xy2 + -1y3 + -1y5 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1xy2 + -1y3 + -1x + -1y5 = 0 + -1x Reorder the terms: x + -1x + -1xy2 + -1y3 + -1y5 = 0 + -1x Combine like terms: x + -1x = 0 0 + -1xy2 + -1y3 + -1y5 = 0 + -1x -1xy2 + -1y3 + -1y5 = 0 + -1x Remove the zero: -1xy2 + -1y3 + -1y5 = -1x Add 'xy2' to each side of the equation. -1xy2 + -1y3 + xy2 + -1y5 = -1x + xy2 Reorder the terms: -1xy2 + xy2 + -1y3 + -1y5 = -1x + xy2 Combine like terms: -1xy2 + xy2 = 0 0 + -1y3 + -1y5 = -1x + xy2 -1y3 + -1y5 = -1x + xy2 Add 'y3' to each side of the equation. -1y3 + y3 + -1y5 = -1x + xy2 + y3 Combine like terms: -1y3 + y3 = 0 0 + -1y5 = -1x + xy2 + y3 -1y5 = -1x + xy2 + y3 Add 'y5' to each side of the equation. -1y5 + y5 = -1x + xy2 + y3 + y5 Combine like terms: -1y5 + y5 = 0 0 = -1x + xy2 + y3 + y5 Simplifying 0 = -1x + xy2 + y3 + y5 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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