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Simplifying (xy2 + x) * dx + (yx2 + y) * dy = 0 Reorder the terms: (x + xy2) * dx + (yx2 + y) * dy = 0 Reorder the terms for easier multiplication: dx(x + xy2) + (yx2 + y) * dy = 0 (x * dx + xy2 * dx) + (yx2 + y) * dy = 0 (dx2 + dx2y2) + (yx2 + y) * dy = 0 Reorder the terms for easier multiplication: dx2 + dx2y2 + dy(x2y + y) = 0 dx2 + dx2y2 + (x2y * dy + y * dy) = 0 dx2 + dx2y2 + (dx2y2 + dy2) = 0 Combine like terms: dx2y2 + dx2y2 = 2dx2y2 dx2 + 2dx2y2 + dy2 = 0 Solving dx2 + 2dx2y2 + dy2 = 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 + 2x2y2 + y2) = 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 '(x2 + 2x2y2 + y2)' equal to zero and attempt to solve: Simplifying x2 + 2x2y2 + y2 = 0 Solving x2 + 2x2y2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + 2x2y2 + -1x2 + y2 = 0 + -1x2 Reorder the terms: x2 + -1x2 + 2x2y2 + y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2x2y2 + y2 = 0 + -1x2 2x2y2 + y2 = 0 + -1x2 Remove the zero: 2x2y2 + y2 = -1x2 Add '-2x2y2' to each side of the equation. 2x2y2 + -2x2y2 + y2 = -1x2 + -2x2y2 Combine like terms: 2x2y2 + -2x2y2 = 0 0 + y2 = -1x2 + -2x2y2 y2 = -1x2 + -2x2y2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1x2 + -2x2y2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x2 + -2x2y2 + -1y2 Simplifying 0 = -1x2 + -2x2y2 + -1y2 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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