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