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Simplifying (x + -1y * ln(y) + y * ln(x)) * dx + x(ln(y) + -1ln(x)) * dx = 0 Multiply y * ln (x + -1lny * y + y * ln(x)) * dx + x(ln(y) + -1ln(x)) * dx = 0 Multiply lny * y (x + -1lny2 + y * ln(x)) * dx + x(ln(y) + -1ln(x)) * dx = 0 Multiply y * ln (x + -1lny2 + lny * x) * dx + x(ln(y) + -1ln(x)) * dx = 0 Multiply lny * x (x + -1lny2 + lnxy) * dx + x(ln(y) + -1ln(x)) * dx = 0 Reorder the terms: (lnxy + -1lny2 + x) * dx + x(ln(y) + -1ln(x)) * dx = 0 Reorder the terms for easier multiplication: dx(lnxy + -1lny2 + x) + x(ln(y) + -1ln(x)) * dx = 0 (lnxy * dx + -1lny2 * dx + x * dx) + x(ln(y) + -1ln(x)) * dx = 0 Reorder the terms: (-1dlnxy2 + dlnx2y + dx2) + x(ln(y) + -1ln(x)) * dx = 0 (-1dlnxy2 + dlnx2y + dx2) + x(ln(y) + -1ln(x)) * dx = 0 Multiply ln * y -1dlnxy2 + dlnx2y + dx2 + x(lny + -1ln(x)) * dx = 0 Multiply ln * x -1dlnxy2 + dlnx2y + dx2 + x(lny + -1lnx) * dx = 0 Reorder the terms: -1dlnxy2 + dlnx2y + dx2 + x(-1lnx + lny) * dx = 0 Reorder the terms for easier multiplication: -1dlnxy2 + dlnx2y + dx2 + x * dx(-1lnx + lny) = 0 Multiply x * dx -1dlnxy2 + dlnx2y + dx2 + dx2(-1lnx + lny) = 0 -1dlnxy2 + dlnx2y + dx2 + (-1lnx * dx2 + lny * dx2) = 0 Reorder the terms: -1dlnxy2 + dlnx2y + dx2 + (dlnx2y + -1dlnx3) = 0 -1dlnxy2 + dlnx2y + dx2 + (dlnx2y + -1dlnx3) = 0 Reorder the terms: -1dlnxy2 + dlnx2y + dlnx2y + -1dlnx3 + dx2 = 0 Combine like terms: dlnx2y + dlnx2y = 2dlnx2y -1dlnxy2 + 2dlnx2y + -1dlnx3 + dx2 = 0 Solving -1dlnxy2 + 2dlnx2y + -1dlnx3 + dx2 = 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), 'dx'. dx(-1lny2 + 2lnxy + -1lnx2 + x) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(-1lny2 + 2lnxy + -1lnx2 + x)' equal to zero and attempt to solve: Simplifying -1lny2 + 2lnxy + -1lnx2 + x = 0 Reorder the terms: 2lnxy + -1lnx2 + -1lny2 + x = 0 Solving 2lnxy + -1lnx2 + -1lny2 + x = 0 Move all terms containing d to the left, all other terms to the right. Add '-2lnxy' to each side of the equation. 2lnxy + -1lnx2 + -1lny2 + -2lnxy + x = 0 + -2lnxy Reorder the terms: 2lnxy + -2lnxy + -1lnx2 + -1lny2 + x = 0 + -2lnxy Combine like terms: 2lnxy + -2lnxy = 0 0 + -1lnx2 + -1lny2 + x = 0 + -2lnxy -1lnx2 + -1lny2 + x = 0 + -2lnxy Remove the zero: -1lnx2 + -1lny2 + x = -2lnxy Add 'lnx2' to each side of the equation. -1lnx2 + -1lny2 + lnx2 + x = -2lnxy + lnx2 Reorder the terms: -1lnx2 + lnx2 + -1lny2 + x = -2lnxy + lnx2 Combine like terms: -1lnx2 + lnx2 = 0 0 + -1lny2 + x = -2lnxy + lnx2 -1lny2 + x = -2lnxy + lnx2 Add 'lny2' to each side of the equation. -1lny2 + lny2 + x = -2lnxy + lnx2 + lny2 Combine like terms: -1lny2 + lny2 = 0 0 + x = -2lnxy + lnx2 + lny2 x = -2lnxy + lnx2 + lny2 Add '-1x' to each side of the equation. x + -1x = -2lnxy + lnx2 + lny2 + -1x Combine like terms: x + -1x = 0 0 = -2lnxy + lnx2 + lny2 + -1x Simplifying 0 = -2lnxy + lnx2 + lny2 + -1x 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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