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Simplifying (lnx + -1lny) * dy + -1ydx = 0 Reorder the terms for easier multiplication: dy(lnx + -1lny) + -1ydx = 0 (lnx * dy + -1lny * dy) + -1ydx = 0 (dlnxy + -1dlny2) + -1ydx = 0 Solving dlnxy + -1dlny2 + -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), 'dy'. dy(lnx + -1lny + -1x) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(lnx + -1lny + -1x)' equal to zero and attempt to solve: Simplifying lnx + -1lny + -1x = 0 Solving lnx + -1lny + -1x = 0 Move all terms containing d to the left, all other terms to the right. Add '-1lnx' to each side of the equation. lnx + -1lny + -1lnx + -1x = 0 + -1lnx Reorder the terms: lnx + -1lnx + -1lny + -1x = 0 + -1lnx Combine like terms: lnx + -1lnx = 0 0 + -1lny + -1x = 0 + -1lnx -1lny + -1x = 0 + -1lnx Remove the zero: -1lny + -1x = -1lnx Add 'lny' to each side of the equation. -1lny + lny + -1x = -1lnx + lny Combine like terms: -1lny + lny = 0 0 + -1x = -1lnx + lny -1x = -1lnx + lny Add 'x' to each side of the equation. -1x + x = -1lnx + lny + x Combine like terms: -1x + x = 0 0 = -1lnx + lny + x Simplifying 0 = -1lnx + lny + x 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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