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Simplifying (xy2 + x) * dx + (xy2 + y) * dy = 0 Reorder the terms: (x + xy2) * dx + (xy2 + y) * dy = 0 Reorder the terms for easier multiplication: dx(x + xy2) + (xy2 + y) * dy = 0 (x * dx + xy2 * dx) + (xy2 + y) * dy = 0 (dx2 + dx2y2) + (xy2 + y) * dy = 0 Reorder the terms for easier multiplication: dx2 + dx2y2 + dy(xy2 + y) = 0 dx2 + dx2y2 + (xy2 * dy + y * dy) = 0 dx2 + dx2y2 + (dxy3 + dy2) = 0 Reorder the terms: dxy3 + dx2 + dx2y2 + dy2 = 0 Solving dxy3 + dx2 + dx2y2 + 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(xy3 + x2 + x2y2 + 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 '(xy3 + x2 + x2y2 + y2)' equal to zero and attempt to solve: Simplifying xy3 + x2 + x2y2 + y2 = 0 Solving xy3 + x2 + x2y2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy3' to each side of the equation. xy3 + x2 + x2y2 + -1xy3 + y2 = 0 + -1xy3 Reorder the terms: xy3 + -1xy3 + x2 + x2y2 + y2 = 0 + -1xy3 Combine like terms: xy3 + -1xy3 = 0 0 + x2 + x2y2 + y2 = 0 + -1xy3 x2 + x2y2 + y2 = 0 + -1xy3 Remove the zero: x2 + x2y2 + y2 = -1xy3 Add '-1x2' to each side of the equation. x2 + x2y2 + -1x2 + y2 = -1xy3 + -1x2 Reorder the terms: x2 + -1x2 + x2y2 + y2 = -1xy3 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y2 + y2 = -1xy3 + -1x2 x2y2 + y2 = -1xy3 + -1x2 Add '-1x2y2' to each side of the equation. x2y2 + -1x2y2 + y2 = -1xy3 + -1x2 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + y2 = -1xy3 + -1x2 + -1x2y2 y2 = -1xy3 + -1x2 + -1x2y2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1xy3 + -1x2 + -1x2y2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1xy3 + -1x2 + -1x2y2 + -1y2 Simplifying 0 = -1xy3 + -1x2 + -1x2y2 + -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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