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Simplifying x(1 + y2) * dx + -1y(1 + 2x) * dy = 0 Reorder the terms for easier multiplication: x * dx(1 + y2) + -1y(1 + 2x) * dy = 0 Multiply x * dx dx2(1 + y2) + -1y(1 + 2x) * dy = 0 (1 * dx2 + y2 * dx2) + -1y(1 + 2x) * dy = 0 (1dx2 + dx2y2) + -1y(1 + 2x) * dy = 0 Reorder the terms for easier multiplication: 1dx2 + dx2y2 + -1y * dy(1 + 2x) = 0 Multiply y * dy 1dx2 + dx2y2 + -1dy2(1 + 2x) = 0 1dx2 + dx2y2 + (1 * -1dy2 + 2x * -1dy2) = 0 Reorder the terms: 1dx2 + dx2y2 + (-2dxy2 + -1dy2) = 0 1dx2 + dx2y2 + (-2dxy2 + -1dy2) = 0 Reorder the terms: -2dxy2 + 1dx2 + dx2y2 + -1dy2 = 0 Solving -2dxy2 + 1dx2 + dx2y2 + -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(-2xy2 + x2 + x2y2 + -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 '(-2xy2 + x2 + x2y2 + -1y2)' equal to zero and attempt to solve: Simplifying -2xy2 + x2 + x2y2 + -1y2 = 0 Solving -2xy2 + x2 + x2y2 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '2xy2' to each side of the equation. -2xy2 + x2 + x2y2 + 2xy2 + -1y2 = 0 + 2xy2 Reorder the terms: -2xy2 + 2xy2 + x2 + x2y2 + -1y2 = 0 + 2xy2 Combine like terms: -2xy2 + 2xy2 = 0 0 + x2 + x2y2 + -1y2 = 0 + 2xy2 x2 + x2y2 + -1y2 = 0 + 2xy2 Remove the zero: x2 + x2y2 + -1y2 = 2xy2 Add '-1x2' to each side of the equation. x2 + x2y2 + -1x2 + -1y2 = 2xy2 + -1x2 Reorder the terms: x2 + -1x2 + x2y2 + -1y2 = 2xy2 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y2 + -1y2 = 2xy2 + -1x2 x2y2 + -1y2 = 2xy2 + -1x2 Add '-1x2y2' to each side of the equation. x2y2 + -1x2y2 + -1y2 = 2xy2 + -1x2 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + -1y2 = 2xy2 + -1x2 + -1x2y2 -1y2 = 2xy2 + -1x2 + -1x2y2 Add 'y2' to each side of the equation. -1y2 + y2 = 2xy2 + -1x2 + -1x2y2 + y2 Combine like terms: -1y2 + y2 = 0 0 = 2xy2 + -1x2 + -1x2y2 + y2 Simplifying 0 = 2xy2 + -1x2 + -1x2y2 + 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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