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Simplifying y * lnydx + (2 + -1x + -1x2) * dy = 0 Multiply y * dlnxy dlnxy2 + (2 + -1x + -1x2) * dy = 0 Reorder the terms for easier multiplication: dlnxy2 + dy(2 + -1x + -1x2) = 0 dlnxy2 + (2 * dy + -1x * dy + -1x2 * dy) = 0 Reorder the terms: dlnxy2 + (-1dxy + -1dx2y + 2dy) = 0 dlnxy2 + (-1dxy + -1dx2y + 2dy) = 0 Solving dlnxy2 + -1dxy + -1dx2y + 2dy = 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(lnxy + -1x + -1x2 + 2) = 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 '(lnxy + -1x + -1x2 + 2)' equal to zero and attempt to solve: Simplifying lnxy + -1x + -1x2 + 2 = 0 Reorder the terms: 2 + lnxy + -1x + -1x2 = 0 Solving 2 + lnxy + -1x + -1x2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + lnxy + -1x + -2 + -1x2 = 0 + -2 Reorder the terms: 2 + -2 + lnxy + -1x + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + lnxy + -1x + -1x2 = 0 + -2 lnxy + -1x + -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 lnxy + -1x + -1x2 = -2 Add '-1lnxy' to each side of the equation. lnxy + -1x + -1lnxy + -1x2 = -2 + -1lnxy Reorder the terms: lnxy + -1lnxy + -1x + -1x2 = -2 + -1lnxy Combine like terms: lnxy + -1lnxy = 0 0 + -1x + -1x2 = -2 + -1lnxy -1x + -1x2 = -2 + -1lnxy Add 'x' to each side of the equation. -1x + x + -1x2 = -2 + -1lnxy + x Combine like terms: -1x + x = 0 0 + -1x2 = -2 + -1lnxy + x -1x2 = -2 + -1lnxy + x Add 'x2' to each side of the equation. -1x2 + x2 = -2 + -1lnxy + x + x2 Combine like terms: -1x2 + x2 = 0 0 = -2 + -1lnxy + x + x2 Simplifying 0 = -2 + -1lnxy + x + x2 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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