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Simplifying (y + -1ln(x)) * dx + xln(x) * dy = 0 Multiply ln * x (y + -1lnx) * dx + xln(x) * dy = 0 Reorder the terms: (-1lnx + y) * dx + xln(x) * dy = 0 Reorder the terms for easier multiplication: dx(-1lnx + y) + xln(x) * dy = 0 (-1lnx * dx + y * dx) + xln(x) * dy = 0 (-1dlnx2 + dxy) + xln(x) * dy = 0 Multiply lnx * x -1dlnx2 + dxy + lnx2 * dy = 0 Multiply lnx2 * dy -1dlnx2 + dxy + dlnx2y = 0 Reorder the terms: -1dlnx2 + dlnx2y + dxy = 0 Solving -1dlnx2 + dlnx2y + dxy = 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(-1lnx + lnxy + y) = 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 '(-1lnx + lnxy + y)' equal to zero and attempt to solve: Simplifying -1lnx + lnxy + y = 0 Solving -1lnx + lnxy + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'lnx' to each side of the equation. -1lnx + lnxy + lnx + y = 0 + lnx Reorder the terms: -1lnx + lnx + lnxy + y = 0 + lnx Combine like terms: -1lnx + lnx = 0 0 + lnxy + y = 0 + lnx lnxy + y = 0 + lnx Remove the zero: lnxy + y = lnx Add '-1lnxy' to each side of the equation. lnxy + -1lnxy + y = lnx + -1lnxy Combine like terms: lnxy + -1lnxy = 0 0 + y = lnx + -1lnxy y = lnx + -1lnxy Add '-1y' to each side of the equation. y + -1y = lnx + -1lnxy + -1y Combine like terms: y + -1y = 0 0 = lnx + -1lnxy + -1y Simplifying 0 = lnx + -1lnxy + -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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