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Simplifying y(1 + x2) * dx + x(1 + y2) * dy = 0 Reorder the terms for easier multiplication: y * dx(1 + x2) + x(1 + y2) * dy = 0 Multiply y * dx dxy(1 + x2) + x(1 + y2) * dy = 0 (1 * dxy + x2 * dxy) + x(1 + y2) * dy = 0 (1dxy + dx3y) + x(1 + y2) * dy = 0 Reorder the terms for easier multiplication: 1dxy + dx3y + x * dy(1 + y2) = 0 Multiply x * dy 1dxy + dx3y + dxy(1 + y2) = 0 1dxy + dx3y + (1 * dxy + y2 * dxy) = 0 1dxy + dx3y + (1dxy + dxy3) = 0 Reorder the terms: 1dxy + 1dxy + dxy3 + dx3y = 0 Combine like terms: 1dxy + 1dxy = 2dxy 2dxy + dxy3 + dx3y = 0 Solving 2dxy + dxy3 + dx3y = 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), 'dxy'. dxy(2 + y2 + x2) = 0 Factor a trinomial. dxy((y + x)(y + x)) = 0Subproblem 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.Subproblem 3
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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