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Simplifying (x + -1y * lny + y * lnx) * dx + x(lnx + -1lnx) * dy = 0 Multiply y * lny (x + -1lny2 + y * lnx) * dx + x(lnx + -1lnx) * dy = 0 Multiply y * lnx (x + -1lny2 + lnxy) * dx + x(lnx + -1lnx) * dy = 0 Reorder the terms: (lnxy + -1lny2 + x) * dx + x(lnx + -1lnx) * dy = 0 Reorder the terms for easier multiplication: dx(lnxy + -1lny2 + x) + x(lnx + -1lnx) * dy = 0 (lnxy * dx + -1lny2 * dx + x * dx) + x(lnx + -1lnx) * dy = 0 Reorder the terms: (-1dlnxy2 + dlnx2y + dx2) + x(lnx + -1lnx) * dy = 0 (-1dlnxy2 + dlnx2y + dx2) + x(lnx + -1lnx) * dy = 0 Combine like terms: lnx + -1lnx = 0 -1dlnxy2 + dlnx2y + dx2 + x(0) * dy = 0 Reorder the terms for easier multiplication: -1dlnxy2 + dlnx2y + dx2 + 0x * dy = 0 Anything times zero is zero. -1dlnxy2 + dlnx2y + dx2 + 0x * dy = 0 Reorder the terms: 0 + -1dlnxy2 + dlnx2y + dx2 = 0 Remove the zero: -1dlnxy2 + dlnx2y + dx2 = 0 Solving -1dlnxy2 + dlnx2y + dx2 = 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(-1lny2 + lnxy + x) = 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 '(-1lny2 + lnxy + x)' equal to zero and attempt to solve: Simplifying -1lny2 + lnxy + x = 0 Reorder the terms: lnxy + -1lny2 + x = 0 Solving lnxy + -1lny2 + x = 0 Move all terms containing d to the left, all other terms to the right. Add '-1lnxy' to each side of the equation. lnxy + -1lny2 + -1lnxy + x = 0 + -1lnxy Reorder the terms: lnxy + -1lnxy + -1lny2 + x = 0 + -1lnxy Combine like terms: lnxy + -1lnxy = 0 0 + -1lny2 + x = 0 + -1lnxy -1lny2 + x = 0 + -1lnxy Remove the zero: -1lny2 + x = -1lnxy Add 'lny2' to each side of the equation. -1lny2 + lny2 + x = -1lnxy + lny2 Combine like terms: -1lny2 + lny2 = 0 0 + x = -1lnxy + lny2 x = -1lnxy + lny2 Add '-1x' to each side of the equation. x + -1x = -1lnxy + lny2 + -1x Combine like terms: x + -1x = 0 0 = -1lnxy + lny2 + -1x Simplifying 0 = -1lnxy + lny2 + -1x 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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