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Simplifying (xlny + xy) * dx + (ylnx + xy) * dy = 0 Reorder the terms for easier multiplication: dx(lnxy + xy) + (ylnx + xy) * dy = 0 (lnxy * dx + xy * dx) + (ylnx + xy) * dy = 0 (dlnx2y + dx2y) + (ylnx + xy) * dy = 0 Reorder the terms for easier multiplication: dlnx2y + dx2y + dy(lnxy + xy) = 0 dlnx2y + dx2y + (lnxy * dy + xy * dy) = 0 dlnx2y + dx2y + (dlnxy2 + dxy2) = 0 Reorder the terms: dlnxy2 + dlnx2y + dxy2 + dx2y = 0 Solving dlnxy2 + 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(lny + 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 '(lny + lnx + y + x)' equal to zero and attempt to solve: Simplifying lny + lnx + y + x = 0 Reorder the terms: lnx + lny + x + y = 0 Solving lnx + lny + x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1lnx' to each side of the equation. lnx + lny + x + -1lnx + y = 0 + -1lnx Reorder the terms: lnx + -1lnx + lny + x + y = 0 + -1lnx Combine like terms: lnx + -1lnx = 0 0 + lny + x + y = 0 + -1lnx lny + x + y = 0 + -1lnx Remove the zero: lny + x + y = -1lnx Add '-1lny' to each side of the equation. lny + x + -1lny + y = -1lnx + -1lny Reorder the terms: lny + -1lny + x + y = -1lnx + -1lny Combine like terms: lny + -1lny = 0 0 + x + y = -1lnx + -1lny x + y = -1lnx + -1lny Add '-1x' to each side of the equation. x + -1x + y = -1lnx + -1lny + -1x Combine like terms: x + -1x = 0 0 + y = -1lnx + -1lny + -1x y = -1lnx + -1lny + -1x Add '-1y' to each side of the equation. y + -1y = -1lnx + -1lny + -1x + -1y Combine like terms: y + -1y = 0 0 = -1lnx + -1lny + -1x + -1y Simplifying 0 = -1lnx + -1lny + -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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