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Simplifying y(x + y) * dx + (xy + 1) * dy = 0 Reorder the terms for easier multiplication: y * dx(x + y) + (xy + 1) * dy = 0 Multiply y * dx dxy(x + y) + (xy + 1) * dy = 0 (x * dxy + y * dxy) + (xy + 1) * dy = 0 Reorder the terms: (dxy2 + dx2y) + (xy + 1) * dy = 0 (dxy2 + dx2y) + (xy + 1) * dy = 0 Reorder the terms: dxy2 + dx2y + (1 + xy) * dy = 0 Reorder the terms for easier multiplication: dxy2 + dx2y + dy(1 + xy) = 0 dxy2 + dx2y + (1 * dy + xy * dy) = 0 Reorder the terms: dxy2 + dx2y + (dxy2 + 1dy) = 0 dxy2 + dx2y + (dxy2 + 1dy) = 0 Reorder the terms: dxy2 + dxy2 + dx2y + 1dy = 0 Combine like terms: dxy2 + dxy2 = 2dxy2 2dxy2 + dx2y + 1dy = 0 Solving 2dxy2 + dx2y + 1dy = 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), 'dy'. dy(2xy + x2 + 1) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(2xy + x2 + 1)' equal to zero and attempt to solve: Simplifying 2xy + x2 + 1 = 0 Reorder the terms: 1 + 2xy + x2 = 0 Solving 1 + 2xy + x2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2xy + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2xy + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2xy + x2 = 0 + -1 2xy + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2xy + x2 = -1 Add '-2xy' to each side of the equation. 2xy + -2xy + x2 = -1 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 = -1 + -2xy x2 = -1 + -2xy Add '-1x2' to each side of the equation. x2 + -1x2 = -1 + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -1 + -2xy + -1x2 Simplifying 0 = -1 + -2xy + -1x2 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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