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Simplifying 2xdy = (y2 + -1)(dy + -1dx) Reorder the terms: 2dxy = (-1 + y2)(dy + -1dx) Reorder the terms: 2dxy = (-1 + y2)(-1dx + dy) Multiply (-1 + y2) * (-1dx + dy) 2dxy = (-1(-1dx + dy) + y2(-1dx + dy)) 2dxy = ((-1dx * -1 + dy * -1) + y2(-1dx + dy)) 2dxy = ((1dx + -1dy) + y2(-1dx + dy)) 2dxy = (1dx + -1dy + (-1dx * y2 + dy * y2)) 2dxy = (1dx + -1dy + (-1dxy2 + dy3)) Reorder the terms: 2dxy = (1dx + -1dxy2 + -1dy + dy3) 2dxy = (1dx + -1dxy2 + -1dy + dy3) Solving 2dxy = 1dx + -1dxy2 + -1dy + dy3 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 + 2dxy = 1dx + -1dxy2 + -1dy + -1dx + dy3 Reorder the terms: -1dx + 2dxy = 1dx + -1dx + -1dxy2 + -1dy + dy3 Combine like terms: 1dx + -1dx = 0 -1dx + 2dxy = 0 + -1dxy2 + -1dy + dy3 -1dx + 2dxy = -1dxy2 + -1dy + dy3 Add 'dxy2' to each side of the equation. -1dx + 2dxy + dxy2 = -1dxy2 + -1dy + dxy2 + dy3 Reorder the terms: -1dx + 2dxy + dxy2 = -1dxy2 + dxy2 + -1dy + dy3 Combine like terms: -1dxy2 + dxy2 = 0 -1dx + 2dxy + dxy2 = 0 + -1dy + dy3 -1dx + 2dxy + dxy2 = -1dy + dy3 Add 'dy' to each side of the equation. -1dx + 2dxy + dxy2 + dy = -1dy + dy + dy3 Combine like terms: -1dy + dy = 0 -1dx + 2dxy + dxy2 + dy = 0 + dy3 -1dx + 2dxy + dxy2 + dy = dy3 Add '-1dy3' to each side of the equation. -1dx + 2dxy + dxy2 + dy + -1dy3 = dy3 + -1dy3 Combine like terms: dy3 + -1dy3 = 0 -1dx + 2dxy + dxy2 + dy + -1dy3 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + 2xy + xy2 + y + -1y3) = 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 + 2xy + xy2 + y + -1y3)' equal to zero and attempt to solve: Simplifying -1x + 2xy + xy2 + y + -1y3 = 0 Solving -1x + 2xy + xy2 + y + -1y3 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 2xy + xy2 + y + x + -1y3 = 0 + x Reorder the terms: -1x + x + 2xy + xy2 + y + -1y3 = 0 + x Combine like terms: -1x + x = 0 0 + 2xy + xy2 + y + -1y3 = 0 + x 2xy + xy2 + y + -1y3 = 0 + x Remove the zero: 2xy + xy2 + y + -1y3 = x Add '-2xy' to each side of the equation. 2xy + xy2 + y + -2xy + -1y3 = x + -2xy Reorder the terms: 2xy + -2xy + xy2 + y + -1y3 = x + -2xy Combine like terms: 2xy + -2xy = 0 0 + xy2 + y + -1y3 = x + -2xy xy2 + y + -1y3 = x + -2xy Add '-1xy2' to each side of the equation. xy2 + y + -1xy2 + -1y3 = x + -2xy + -1xy2 Reorder the terms: xy2 + -1xy2 + y + -1y3 = x + -2xy + -1xy2 Combine like terms: xy2 + -1xy2 = 0 0 + y + -1y3 = x + -2xy + -1xy2 y + -1y3 = x + -2xy + -1xy2 Add '-1y' to each side of the equation. y + -1y + -1y3 = x + -2xy + -1xy2 + -1y Combine like terms: y + -1y = 0 0 + -1y3 = x + -2xy + -1xy2 + -1y -1y3 = x + -2xy + -1xy2 + -1y Add 'y3' to each side of the equation. -1y3 + y3 = x + -2xy + -1xy2 + -1y + y3 Combine like terms: -1y3 + y3 = 0 0 = x + -2xy + -1xy2 + -1y + y3 Simplifying 0 = x + -2xy + -1xy2 + -1y + y3 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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