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Simplifying ydx = (2x + 1)(dx + -1dy) Reorder the terms: dxy = (1 + 2x)(dx + -1dy) Multiply (1 + 2x) * (dx + -1dy) dxy = (1(dx + -1dy) + 2x * (dx + -1dy)) dxy = ((dx * 1 + -1dy * 1) + 2x * (dx + -1dy)) dxy = ((1dx + -1dy) + 2x * (dx + -1dy)) dxy = (1dx + -1dy + (dx * 2x + -1dy * 2x)) Reorder the terms: dxy = (1dx + -1dy + (-2dxy + 2dx2)) dxy = (1dx + -1dy + (-2dxy + 2dx2)) Reorder the terms: dxy = (1dx + -2dxy + 2dx2 + -1dy) dxy = (1dx + -2dxy + 2dx2 + -1dy) Solving dxy = 1dx + -2dxy + 2dx2 + -1dy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. -1dx + dxy = 1dx + -2dxy + 2dx2 + -1dx + -1dy Reorder the terms: -1dx + dxy = 1dx + -1dx + -2dxy + 2dx2 + -1dy Combine like terms: 1dx + -1dx = 0 -1dx + dxy = 0 + -2dxy + 2dx2 + -1dy -1dx + dxy = -2dxy + 2dx2 + -1dy Add '2dxy' to each side of the equation. -1dx + dxy + 2dxy = -2dxy + 2dx2 + 2dxy + -1dy Combine like terms: dxy + 2dxy = 3dxy -1dx + 3dxy = -2dxy + 2dx2 + 2dxy + -1dy Reorder the terms: -1dx + 3dxy = -2dxy + 2dxy + 2dx2 + -1dy Combine like terms: -2dxy + 2dxy = 0 -1dx + 3dxy = 0 + 2dx2 + -1dy -1dx + 3dxy = 2dx2 + -1dy Add '-2dx2' to each side of the equation. -1dx + 3dxy + -2dx2 = 2dx2 + -2dx2 + -1dy Combine like terms: 2dx2 + -2dx2 = 0 -1dx + 3dxy + -2dx2 = 0 + -1dy -1dx + 3dxy + -2dx2 = -1dy Add 'dy' to each side of the equation. -1dx + 3dxy + -2dx2 + dy = -1dy + dy Combine like terms: -1dy + dy = 0 -1dx + 3dxy + -2dx2 + dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + 3xy + -2x2 + 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 '(-1x + 3xy + -2x2 + y)' equal to zero and attempt to solve: Simplifying -1x + 3xy + -2x2 + y = 0 Solving -1x + 3xy + -2x2 + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 3xy + -2x2 + x + y = 0 + x Reorder the terms: -1x + x + 3xy + -2x2 + y = 0 + x Combine like terms: -1x + x = 0 0 + 3xy + -2x2 + y = 0 + x 3xy + -2x2 + y = 0 + x Remove the zero: 3xy + -2x2 + y = x Add '-3xy' to each side of the equation. 3xy + -2x2 + -3xy + y = x + -3xy Reorder the terms: 3xy + -3xy + -2x2 + y = x + -3xy Combine like terms: 3xy + -3xy = 0 0 + -2x2 + y = x + -3xy -2x2 + y = x + -3xy Add '2x2' to each side of the equation. -2x2 + 2x2 + y = x + -3xy + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + y = x + -3xy + 2x2 y = x + -3xy + 2x2 Add '-1y' to each side of the equation. y + -1y = x + -3xy + 2x2 + -1y Combine like terms: y + -1y = 0 0 = x + -3xy + 2x2 + -1y Simplifying 0 = x + -3xy + 2x2 + -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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