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Simplifying (y + x2y) * dy = (x2y + -1x) * dx Reorder the terms: (x2y + y) * dy = (x2y + -1x) * dx Reorder the terms for easier multiplication: dy(x2y + y) = (x2y + -1x) * dx (x2y * dy + y * dy) = (x2y + -1x) * dx (dx2y2 + dy2) = (x2y + -1x) * dx Reorder the terms: dx2y2 + dy2 = (-1x + x2y) * dx Reorder the terms for easier multiplication: dx2y2 + dy2 = dx(-1x + x2y) dx2y2 + dy2 = (-1x * dx + x2y * dx) dx2y2 + dy2 = (-1dx2 + dx3y) Solving dx2y2 + dy2 = -1dx2 + dx3y Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add 'dx2' to each side of the equation. dx2y2 + dx2 + dy2 = -1dx2 + dx2 + dx3y Reorder the terms: dx2 + dx2y2 + dy2 = -1dx2 + dx2 + dx3y Combine like terms: -1dx2 + dx2 = 0 dx2 + dx2y2 + dy2 = 0 + dx3y dx2 + dx2y2 + dy2 = dx3y Add '-1dx3y' to each side of the equation. dx2 + dx2y2 + -1dx3y + dy2 = dx3y + -1dx3y Combine like terms: dx3y + -1dx3y = 0 dx2 + dx2y2 + -1dx3y + dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x2 + x2y2 + -1x3y + 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 + x2y2 + -1x3y + y2)' equal to zero and attempt to solve: Simplifying x2 + x2y2 + -1x3y + y2 = 0 Solving x2 + x2y2 + -1x3y + 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 + x2y2 + -1x3y + -1x2 + y2 = 0 + -1x2 Reorder the terms: x2 + -1x2 + x2y2 + -1x3y + y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y2 + -1x3y + y2 = 0 + -1x2 x2y2 + -1x3y + y2 = 0 + -1x2 Remove the zero: x2y2 + -1x3y + y2 = -1x2 Add '-1x2y2' to each side of the equation. x2y2 + -1x3y + -1x2y2 + y2 = -1x2 + -1x2y2 Reorder the terms: x2y2 + -1x2y2 + -1x3y + y2 = -1x2 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + -1x3y + y2 = -1x2 + -1x2y2 -1x3y + y2 = -1x2 + -1x2y2 Add 'x3y' to each side of the equation. -1x3y + x3y + y2 = -1x2 + -1x2y2 + x3y Combine like terms: -1x3y + x3y = 0 0 + y2 = -1x2 + -1x2y2 + x3y y2 = -1x2 + -1x2y2 + x3y Add '-1y2' to each side of the equation. y2 + -1y2 = -1x2 + -1x2y2 + x3y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x2 + -1x2y2 + x3y + -1y2 Simplifying 0 = -1x2 + -1x2y2 + x3y + -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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