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Simplifying (x + -1y) * dy + (y + x + 1) * dx = 0 Reorder the terms for easier multiplication: dy(x + -1y) + (y + x + 1) * dx = 0 (x * dy + -1y * dy) + (y + x + 1) * dx = 0 (dxy + -1dy2) + (y + x + 1) * dx = 0 Reorder the terms: dxy + -1dy2 + (1 + x + y) * dx = 0 Reorder the terms for easier multiplication: dxy + -1dy2 + dx(1 + x + y) = 0 dxy + -1dy2 + (1 * dx + x * dx + y * dx) = 0 Reorder the terms: dxy + -1dy2 + (1dx + dxy + dx2) = 0 dxy + -1dy2 + (1dx + dxy + dx2) = 0 Reorder the terms: 1dx + dxy + dxy + dx2 + -1dy2 = 0 Combine like terms: dxy + dxy = 2dxy 1dx + 2dxy + dx2 + -1dy2 = 0 Solving 1dx + 2dxy + dx2 + -1dy2 = 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 + 2xy + x2 + -1y2) = 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 + x2 + -1y2)' equal to zero and attempt to solve: Simplifying x + 2xy + x2 + -1y2 = 0 Solving x + 2xy + x2 + -1y2 = 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 + x2 + -1x + -1y2 = 0 + -1x Reorder the terms: x + -1x + 2xy + x2 + -1y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 2xy + x2 + -1y2 = 0 + -1x 2xy + x2 + -1y2 = 0 + -1x Remove the zero: 2xy + x2 + -1y2 = -1x Add '-2xy' to each side of the equation. 2xy + x2 + -2xy + -1y2 = -1x + -2xy Reorder the terms: 2xy + -2xy + x2 + -1y2 = -1x + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + -1y2 = -1x + -2xy x2 + -1y2 = -1x + -2xy Add '-1x2' to each side of the equation. x2 + -1x2 + -1y2 = -1x + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1y2 = -1x + -2xy + -1x2 -1y2 = -1x + -2xy + -1x2 Add 'y2' to each side of the equation. -1y2 + y2 = -1x + -2xy + -1x2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -1x + -2xy + -1x2 + y2 Simplifying 0 = -1x + -2xy + -1x2 + y2 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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