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