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Simplifying (x3 + x2 + x + 1) * dy = (2x2 + x) * dx Reorder the terms: (1 + x + x2 + x3) * dy = (2x2 + x) * dx Reorder the terms for easier multiplication: dy(1 + x + x2 + x3) = (2x2 + x) * dx (1 * dy + x * dy + x2 * dy + x3 * dy) = (2x2 + x) * dx Reorder the terms: (dxy + dx2y + dx3y + 1dy) = (2x2 + x) * dx (dxy + dx2y + dx3y + 1dy) = (2x2 + x) * dx Reorder the terms: dxy + dx2y + dx3y + 1dy = (x + 2x2) * dx Reorder the terms for easier multiplication: dxy + dx2y + dx3y + 1dy = dx(x + 2x2) dxy + dx2y + dx3y + 1dy = (x * dx + 2x2 * dx) dxy + dx2y + dx3y + 1dy = (dx2 + 2dx3) Solving dxy + dx2y + dx3y + 1dy = dx2 + 2dx3 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx2' to each side of the equation. dxy + dx2y + dx3y + -1dx2 + 1dy = dx2 + -1dx2 + 2dx3 Reorder the terms: dxy + -1dx2 + dx2y + dx3y + 1dy = dx2 + -1dx2 + 2dx3 Combine like terms: dx2 + -1dx2 = 0 dxy + -1dx2 + dx2y + dx3y + 1dy = 0 + 2dx3 dxy + -1dx2 + dx2y + dx3y + 1dy = 2dx3 Add '-2dx3' to each side of the equation. dxy + -1dx2 + dx2y + dx3y + -2dx3 + 1dy = 2dx3 + -2dx3 Reorder the terms: dxy + -1dx2 + dx2y + -2dx3 + dx3y + 1dy = 2dx3 + -2dx3 Combine like terms: 2dx3 + -2dx3 = 0 dxy + -1dx2 + dx2y + -2dx3 + dx3y + 1dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(xy + -1x2 + x2y + -2x3 + x3y + y) = 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 '(xy + -1x2 + x2y + -2x3 + x3y + y)' equal to zero and attempt to solve: Simplifying xy + -1x2 + x2y + -2x3 + x3y + y = 0 Solving xy + -1x2 + x2y + -2x3 + x3y + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy' to each side of the equation. xy + -1x2 + x2y + -2x3 + x3y + -1xy + y = 0 + -1xy Reorder the terms: xy + -1xy + -1x2 + x2y + -2x3 + x3y + y = 0 + -1xy Combine like terms: xy + -1xy = 0 0 + -1x2 + x2y + -2x3 + x3y + y = 0 + -1xy -1x2 + x2y + -2x3 + x3y + y = 0 + -1xy Remove the zero: -1x2 + x2y + -2x3 + x3y + y = -1xy Add 'x2' to each side of the equation. -1x2 + x2y + -2x3 + x3y + x2 + y = -1xy + x2 Reorder the terms: -1x2 + x2 + x2y + -2x3 + x3y + y = -1xy + x2 Combine like terms: -1x2 + x2 = 0 0 + x2y + -2x3 + x3y + y = -1xy + x2 x2y + -2x3 + x3y + y = -1xy + x2 Add '-1x2y' to each side of the equation. x2y + -2x3 + x3y + -1x2y + y = -1xy + x2 + -1x2y Reorder the terms: x2y + -1x2y + -2x3 + x3y + y = -1xy + x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + -2x3 + x3y + y = -1xy + x2 + -1x2y -2x3 + x3y + y = -1xy + x2 + -1x2y Add '2x3' to each side of the equation. -2x3 + x3y + 2x3 + y = -1xy + x2 + -1x2y + 2x3 Reorder the terms: -2x3 + 2x3 + x3y + y = -1xy + x2 + -1x2y + 2x3 Combine like terms: -2x3 + 2x3 = 0 0 + x3y + y = -1xy + x2 + -1x2y + 2x3 x3y + y = -1xy + x2 + -1x2y + 2x3 Add '-1x3y' to each side of the equation. x3y + -1x3y + y = -1xy + x2 + -1x2y + 2x3 + -1x3y Combine like terms: x3y + -1x3y = 0 0 + y = -1xy + x2 + -1x2y + 2x3 + -1x3y y = -1xy + x2 + -1x2y + 2x3 + -1x3y Add '-1y' to each side of the equation. y + -1y = -1xy + x2 + -1x2y + 2x3 + -1x3y + -1y Combine like terms: y + -1y = 0 0 = -1xy + x2 + -1x2y + 2x3 + -1x3y + -1y Simplifying 0 = -1xy + x2 + -1x2y + 2x3 + -1x3y + -1y 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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