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Simplifying (y + ylnx) * dx + -1(x + -1xy) * dy = 0 Reorder the terms: (lnxy + y) * dx + -1(x + -1xy) * dy = 0 Reorder the terms for easier multiplication: dx(lnxy + y) + -1(x + -1xy) * dy = 0 (lnxy * dx + y * dx) + -1(x + -1xy) * dy = 0 (dlnx2y + dxy) + -1(x + -1xy) * dy = 0 Reorder the terms for easier multiplication: dlnx2y + dxy + -1dy(x + -1xy) = 0 dlnx2y + dxy + (x * -1dy + -1xy * -1dy) = 0 dlnx2y + dxy + (-1dxy + 1dxy2) = 0 Combine like terms: dxy + -1dxy = 0 dlnx2y + 0 + 1dxy2 = 0 dlnx2y + 1dxy2 = 0 Solving dlnx2y + 1dxy2 = 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(lnx + y) = 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 '(lnx + y)' equal to zero and attempt to solve: Simplifying lnx + y = 0 Solving lnx + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1lnx' to each side of the equation. lnx + -1lnx + y = 0 + -1lnx Combine like terms: lnx + -1lnx = 0 0 + y = 0 + -1lnx y = 0 + -1lnx Remove the zero: y = -1lnx Add '-1y' to each side of the equation. y + -1y = -1lnx + -1y Combine like terms: y + -1y = 0 0 = -1lnx + -1y Simplifying 0 = -1lnx + -1y 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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