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Simplifying (x * y2 + 1) * dx + (x2 * y + -1y) * dy = 0 Multiply x * y2 (xy2 + 1) * dx + (x2 * y + -1y) * dy = 0 Reorder the terms: (1 + xy2) * dx + (x2 * y + -1y) * dy = 0 Reorder the terms for easier multiplication: dx(1 + xy2) + (x2 * y + -1y) * dy = 0 (1 * dx + xy2 * dx) + (x2 * y + -1y) * dy = 0 (1dx + dx2y2) + (x2 * y + -1y) * dy = 0 Multiply x2 * y 1dx + dx2y2 + (x2y + -1y) * dy = 0 Reorder the terms for easier multiplication: 1dx + dx2y2 + dy(x2y + -1y) = 0 1dx + dx2y2 + (x2y * dy + -1y * dy) = 0 1dx + dx2y2 + (dx2y2 + -1dy2) = 0 Combine like terms: dx2y2 + dx2y2 = 2dx2y2 1dx + 2dx2y2 + -1dy2 = 0 Solving 1dx + 2dx2y2 + -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 + 2x2y2 + -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 + 2x2y2 + -1y2)' equal to zero and attempt to solve: Simplifying x + 2x2y2 + -1y2 = 0 Solving x + 2x2y2 + -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 + 2x2y2 + -1x + -1y2 = 0 + -1x Reorder the terms: x + -1x + 2x2y2 + -1y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 2x2y2 + -1y2 = 0 + -1x 2x2y2 + -1y2 = 0 + -1x Remove the zero: 2x2y2 + -1y2 = -1x Add '-2x2y2' to each side of the equation. 2x2y2 + -2x2y2 + -1y2 = -1x + -2x2y2 Combine like terms: 2x2y2 + -2x2y2 = 0 0 + -1y2 = -1x + -2x2y2 -1y2 = -1x + -2x2y2 Add 'y2' to each side of the equation. -1y2 + y2 = -1x + -2x2y2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -1x + -2x2y2 + y2 Simplifying 0 = -1x + -2x2y2 + 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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