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Simplifying 2ydx = (x2 + -1)(dx + -1dy) Reorder the terms: 2dxy = (-1 + x2)(dx + -1dy) Multiply (-1 + x2) * (dx + -1dy) 2dxy = (-1(dx + -1dy) + x2(dx + -1dy)) 2dxy = ((dx * -1 + -1dy * -1) + x2(dx + -1dy)) 2dxy = ((-1dx + 1dy) + x2(dx + -1dy)) 2dxy = (-1dx + 1dy + (dx * x2 + -1dy * x2)) Reorder the terms: 2dxy = (-1dx + 1dy + (-1dx2y + dx3)) 2dxy = (-1dx + 1dy + (-1dx2y + dx3)) Reorder the terms: 2dxy = (-1dx + -1dx2y + dx3 + 1dy) 2dxy = (-1dx + -1dx2y + dx3 + 1dy) Solving 2dxy = -1dx + -1dx2y + dx3 + 1dy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add 'dx' to each side of the equation. dx + 2dxy = -1dx + -1dx2y + dx3 + dx + 1dy Reorder the terms: dx + 2dxy = -1dx + dx + -1dx2y + dx3 + 1dy Combine like terms: -1dx + dx = 0 dx + 2dxy = 0 + -1dx2y + dx3 + 1dy dx + 2dxy = -1dx2y + dx3 + 1dy Add 'dx2y' to each side of the equation. dx + 2dxy + dx2y = -1dx2y + dx3 + dx2y + 1dy Reorder the terms: dx + 2dxy + dx2y = -1dx2y + dx2y + dx3 + 1dy Combine like terms: -1dx2y + dx2y = 0 dx + 2dxy + dx2y = 0 + dx3 + 1dy dx + 2dxy + dx2y = dx3 + 1dy Add '-1dx3' to each side of the equation. dx + 2dxy + dx2y + -1dx3 = dx3 + -1dx3 + 1dy Combine like terms: dx3 + -1dx3 = 0 dx + 2dxy + dx2y + -1dx3 = 0 + 1dy dx + 2dxy + dx2y + -1dx3 = 1dy Add '-1dy' to each side of the equation. dx + 2dxy + dx2y + -1dx3 + -1dy = 1dy + -1dy Combine like terms: 1dy + -1dy = 0 dx + 2dxy + dx2y + -1dx3 + -1dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x + 2xy + x2y + -1x3 + -1y) = 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 + 2xy + x2y + -1x3 + -1y)' equal to zero and attempt to solve: Simplifying x + 2xy + x2y + -1x3 + -1y = 0 Solving x + 2xy + x2y + -1x3 + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 2xy + x2y + -1x3 + -1x + -1y = 0 + -1x Reorder the terms: x + -1x + 2xy + x2y + -1x3 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + 2xy + x2y + -1x3 + -1y = 0 + -1x 2xy + x2y + -1x3 + -1y = 0 + -1x Remove the zero: 2xy + x2y + -1x3 + -1y = -1x Add '-2xy' to each side of the equation. 2xy + x2y + -1x3 + -2xy + -1y = -1x + -2xy Reorder the terms: 2xy + -2xy + x2y + -1x3 + -1y = -1x + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2y + -1x3 + -1y = -1x + -2xy x2y + -1x3 + -1y = -1x + -2xy Add '-1x2y' to each side of the equation. x2y + -1x3 + -1x2y + -1y = -1x + -2xy + -1x2y Reorder the terms: x2y + -1x2y + -1x3 + -1y = -1x + -2xy + -1x2y Combine like terms: x2y + -1x2y = 0 0 + -1x3 + -1y = -1x + -2xy + -1x2y -1x3 + -1y = -1x + -2xy + -1x2y Add 'x3' to each side of the equation. -1x3 + x3 + -1y = -1x + -2xy + -1x2y + x3 Combine like terms: -1x3 + x3 = 0 0 + -1y = -1x + -2xy + -1x2y + x3 -1y = -1x + -2xy + -1x2y + x3 Add 'y' to each side of the equation. -1y + y = -1x + -2xy + -1x2y + x3 + y Combine like terms: -1y + y = 0 0 = -1x + -2xy + -1x2y + x3 + y Simplifying 0 = -1x + -2xy + -1x2y + x3 + y 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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