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Simplifying y2(1 + -1x2) * dx + x(x2y + 2x + y) * dy = 0 Reorder the terms for easier multiplication: y2 * dx(1 + -1x2) + x(x2y + 2x + y) * dy = 0 Multiply y2 * dx dxy2(1 + -1x2) + x(x2y + 2x + y) * dy = 0 (1 * dxy2 + -1x2 * dxy2) + x(x2y + 2x + y) * dy = 0 (1dxy2 + -1dx3y2) + x(x2y + 2x + y) * dy = 0 Reorder the terms: 1dxy2 + -1dx3y2 + x(2x + x2y + y) * dy = 0 Reorder the terms for easier multiplication: 1dxy2 + -1dx3y2 + x * dy(2x + x2y + y) = 0 Multiply x * dy 1dxy2 + -1dx3y2 + dxy(2x + x2y + y) = 0 1dxy2 + -1dx3y2 + (2x * dxy + x2y * dxy + y * dxy) = 0 Reorder the terms: 1dxy2 + -1dx3y2 + (dxy2 + 2dx2y + dx3y2) = 0 1dxy2 + -1dx3y2 + (dxy2 + 2dx2y + dx3y2) = 0 Reorder the terms: 1dxy2 + dxy2 + 2dx2y + -1dx3y2 + dx3y2 = 0 Combine like terms: 1dxy2 + dxy2 = 2dxy2 2dxy2 + 2dx2y + -1dx3y2 + dx3y2 = 0 Combine like terms: -1dx3y2 + dx3y2 = 0 2dxy2 + 2dx2y + 0 = 0 2dxy2 + 2dx2y = 0 Solving 2dxy2 + 2dx2y = 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), '2dxy'. 2dxy(y + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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