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Simplifying (x * y + lny) * dx + (x * y + x * lnx) * dy = 0 Multiply x * y (xy + lny) * dx + (x * y + x * lnx) * dy = 0 Reorder the terms: (lny + xy) * dx + (x * y + x * lnx) * dy = 0 Reorder the terms for easier multiplication: dx(lny + xy) + (x * y + x * lnx) * dy = 0 (lny * dx + xy * dx) + (x * y + x * lnx) * dy = 0 (dlnxy + dx2y) + (x * y + x * lnx) * dy = 0 Multiply x * y dlnxy + dx2y + (xy + x * lnx) * dy = 0 Multiply x * lnx dlnxy + dx2y + (xy + lnx2) * dy = 0 Reorder the terms: dlnxy + dx2y + (lnx2 + xy) * dy = 0 Reorder the terms for easier multiplication: dlnxy + dx2y + dy(lnx2 + xy) = 0 dlnxy + dx2y + (lnx2 * dy + xy * dy) = 0 dlnxy + dx2y + (dlnx2y + dxy2) = 0 Reorder the terms: dlnxy + dlnx2y + dxy2 + dx2y = 0 Solving dlnxy + dlnx2y + dxy2 + dx2y = 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(ln + lnx + 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 '(ln + lnx + y + x)' equal to zero and attempt to solve: Simplifying ln + lnx + y + x = 0 Reorder the terms: ln + lnx + x + y = 0 Solving ln + lnx + x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1ln' to each side of the equation. ln + lnx + x + -1ln + y = 0 + -1ln Reorder the terms: ln + -1ln + lnx + x + y = 0 + -1ln Combine like terms: ln + -1ln = 0 0 + lnx + x + y = 0 + -1ln lnx + x + y = 0 + -1ln Remove the zero: lnx + x + y = -1ln Add '-1lnx' to each side of the equation. lnx + x + -1lnx + y = -1ln + -1lnx Reorder the terms: lnx + -1lnx + x + y = -1ln + -1lnx Combine like terms: lnx + -1lnx = 0 0 + x + y = -1ln + -1lnx x + y = -1ln + -1lnx Add '-1x' to each side of the equation. x + -1x + y = -1ln + -1lnx + -1x Combine like terms: x + -1x = 0 0 + y = -1ln + -1lnx + -1x y = -1ln + -1lnx + -1x Add '-1y' to each side of the equation. y + -1y = -1ln + -1lnx + -1x + -1y Combine like terms: y + -1y = 0 0 = -1ln + -1lnx + -1x + -1y Simplifying 0 = -1ln + -1lnx + -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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