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Simplifying x(1 + y2) * dx + -1y(1 + x2) * dy = 0 Reorder the terms for easier multiplication: x * dx(1 + y2) + -1y(1 + x2) * dy = 0 Multiply x * dx dx2(1 + y2) + -1y(1 + x2) * dy = 0 (1 * dx2 + y2 * dx2) + -1y(1 + x2) * dy = 0 (1dx2 + dx2y2) + -1y(1 + x2) * dy = 0 Reorder the terms for easier multiplication: 1dx2 + dx2y2 + -1y * dy(1 + x2) = 0 Multiply y * dy 1dx2 + dx2y2 + -1dy2(1 + x2) = 0 1dx2 + dx2y2 + (1 * -1dy2 + x2 * -1dy2) = 0 Reorder the terms: 1dx2 + dx2y2 + (-1dx2y2 + -1dy2) = 0 1dx2 + dx2y2 + (-1dx2y2 + -1dy2) = 0 Combine like terms: dx2y2 + -1dx2y2 = 0 1dx2 + 0 + -1dy2 = 0 1dx2 + -1dy2 = 0 Solving 1dx2 + -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(x2 + -1y2) = 0 Factor a difference between two squares. d((x + y)(x + -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 + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -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 + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + 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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