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