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Simplifying y(xy + 1) * dx + x(1 + -1xy + x2y2) * dy = 0 Reorder the terms: y(1 + xy) * dx + x(1 + -1xy + x2y2) * dy = 0 Reorder the terms for easier multiplication: y * dx(1 + xy) + x(1 + -1xy + x2y2) * dy = 0 Multiply y * dx dxy(1 + xy) + x(1 + -1xy + x2y2) * dy = 0 (1 * dxy + xy * dxy) + x(1 + -1xy + x2y2) * dy = 0 (1dxy + dx2y2) + x(1 + -1xy + x2y2) * dy = 0 Reorder the terms for easier multiplication: 1dxy + dx2y2 + x * dy(1 + -1xy + x2y2) = 0 Multiply x * dy 1dxy + dx2y2 + dxy(1 + -1xy + x2y2) = 0 1dxy + dx2y2 + (1 * dxy + -1xy * dxy + x2y2 * dxy) = 0 1dxy + dx2y2 + (1dxy + -1dx2y2 + dx3y3) = 0 Reorder the terms: 1dxy + 1dxy + dx2y2 + -1dx2y2 + dx3y3 = 0 Combine like terms: 1dxy + 1dxy = 2dxy 2dxy + dx2y2 + -1dx2y2 + dx3y3 = 0 Combine like terms: dx2y2 + -1dx2y2 = 0 2dxy + 0 + dx3y3 = 0 2dxy + dx3y3 = 0 Solving 2dxy + dx3y3 = 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 + x2y2) = 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 '(2 + x2y2)' equal to zero and attempt to solve: Simplifying 2 + x2y2 = 0 Solving 2 + x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x2y2 = 0 + -2 x2y2 = 0 + -2 Combine like terms: 0 + -2 = -2 x2y2 = -2 Add '-1x2y2' to each side of the equation. x2y2 + -1x2y2 = -2 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 = -2 + -1x2y2 Simplifying 0 = -2 + -1x2y2 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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