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Simplifying 2(1 + x2) * dy + -1(1 + -1y2) * dx = 0 Reorder the terms for easier multiplication: 2dy(1 + x2) + -1(1 + -1y2) * dx = 0 (1 * 2dy + x2 * 2dy) + -1(1 + -1y2) * dx = 0 Reorder the terms: (2dx2y + 2dy) + -1(1 + -1y2) * dx = 0 (2dx2y + 2dy) + -1(1 + -1y2) * dx = 0 Reorder the terms for easier multiplication: 2dx2y + 2dy + -1dx(1 + -1y2) = 0 2dx2y + 2dy + (1 * -1dx + -1y2 * -1dx) = 0 2dx2y + 2dy + (-1dx + 1dxy2) = 0 Reorder the terms: -1dx + 1dxy2 + 2dx2y + 2dy = 0 Solving -1dx + 1dxy2 + 2dx2y + 2dy = 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(-1x + xy2 + 2x2y + 2y) = 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 + xy2 + 2x2y + 2y)' equal to zero and attempt to solve: Simplifying -1x + xy2 + 2x2y + 2y = 0 Solving -1x + xy2 + 2x2y + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + xy2 + 2x2y + x + 2y = 0 + x Reorder the terms: -1x + x + xy2 + 2x2y + 2y = 0 + x Combine like terms: -1x + x = 0 0 + xy2 + 2x2y + 2y = 0 + x xy2 + 2x2y + 2y = 0 + x Remove the zero: xy2 + 2x2y + 2y = x Add '-1xy2' to each side of the equation. xy2 + 2x2y + -1xy2 + 2y = x + -1xy2 Reorder the terms: xy2 + -1xy2 + 2x2y + 2y = x + -1xy2 Combine like terms: xy2 + -1xy2 = 0 0 + 2x2y + 2y = x + -1xy2 2x2y + 2y = x + -1xy2 Add '-2x2y' to each side of the equation. 2x2y + -2x2y + 2y = x + -1xy2 + -2x2y Combine like terms: 2x2y + -2x2y = 0 0 + 2y = x + -1xy2 + -2x2y 2y = x + -1xy2 + -2x2y Add '-2y' to each side of the equation. 2y + -2y = x + -1xy2 + -2x2y + -2y Combine like terms: 2y + -2y = 0 0 = x + -1xy2 + -2x2y + -2y Simplifying 0 = x + -1xy2 + -2x2y + -2y 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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