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