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Simplifying (y + -1ln(X)) * dx + (X + -1) * dy = 0 Multiply ln * X (y + -1lnX) * dx + (X + -1) * dy = 0 Reorder the terms: (-1lnX + y) * dx + (X + -1) * dy = 0 Reorder the terms for easier multiplication: dx(-1lnX + y) + (X + -1) * dy = 0 (-1lnX * dx + y * dx) + (X + -1) * dy = 0 (-1dlnxX + dxy) + (X + -1) * dy = 0 Reorder the terms: -1dlnxX + dxy + (-1 + X) * dy = 0 Reorder the terms for easier multiplication: -1dlnxX + dxy + dy(-1 + X) = 0 -1dlnxX + dxy + (-1 * dy + X * dy) = 0 -1dlnxX + dxy + (-1dy + dyX) = 0 Solving -1dlnxX + dxy + -1dy + dyX = 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), 'd'. d(-1lnxX + xy + -1y + yX) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-1lnxX + xy + -1y + yX)' equal to zero and attempt to solve: Simplifying -1lnxX + xy + -1y + yX = 0 Solving -1lnxX + xy + -1y + yX = 0 Move all terms containing d to the left, all other terms to the right. Add 'lnxX' to each side of the equation. -1lnxX + xy + -1y + lnxX + yX = 0 + lnxX Reorder the terms: -1lnxX + lnxX + xy + -1y + yX = 0 + lnxX Combine like terms: -1lnxX + lnxX = 0 0 + xy + -1y + yX = 0 + lnxX xy + -1y + yX = 0 + lnxX Remove the zero: xy + -1y + yX = lnxX Add '-1xy' to each side of the equation. xy + -1y + -1xy + yX = lnxX + -1xy Reorder the terms: xy + -1xy + -1y + yX = lnxX + -1xy Combine like terms: xy + -1xy = 0 0 + -1y + yX = lnxX + -1xy -1y + yX = lnxX + -1xy Add 'y' to each side of the equation. -1y + y + yX = lnxX + -1xy + y Combine like terms: -1y + y = 0 0 + yX = lnxX + -1xy + y yX = lnxX + -1xy + y Add '-1yX' to each side of the equation. yX + -1yX = lnxX + -1xy + y + -1yX Combine like terms: yX + -1yX = 0 0 = lnxX + -1xy + y + -1yX Simplifying 0 = lnxX + -1xy + y + -1yX The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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