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Simplifying xdy + -1(y + xy2(1 + lnx)) * dx = 0 dxy + -1(y + (1 * xy2 + lnx * xy2)) * dx = 0 Reorder the terms: dxy + -1(y + (lnx2y2 + 1xy2)) * dx = 0 dxy + -1(y + (lnx2y2 + 1xy2)) * dx = 0 Reorder the terms: dxy + -1(lnx2y2 + 1xy2 + y) * dx = 0 Reorder the terms for easier multiplication: dxy + -1dx(lnx2y2 + 1xy2 + y) = 0 dxy + (lnx2y2 * -1dx + 1xy2 * -1dx + y * -1dx) = 0 Reorder the terms: dxy + (-1dlnx3y2 + -1dxy + -1dx2y2) = 0 dxy + (-1dlnx3y2 + -1dxy + -1dx2y2) = 0 Reorder the terms: -1dlnx3y2 + dxy + -1dxy + -1dx2y2 = 0 Combine like terms: dxy + -1dxy = 0 -1dlnx3y2 + 0 + -1dx2y2 = 0 -1dlnx3y2 + -1dx2y2 = 0 Solving -1dlnx3y2 + -1dx2y2 = 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), '-1dx2y2'. -1dx2y2(lnx + 1) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'dx2y2' equal to zero and attempt to solve: Simplifying dx2y2 = 0 Solving dx2y2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2y2 = 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 + 1)' equal to zero and attempt to solve: Simplifying lnx + 1 = 0 Reorder the terms: 1 + lnx = 0 Solving 1 + lnx = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + lnx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + lnx = 0 + -1 lnx = 0 + -1 Combine like terms: 0 + -1 = -1 lnx = -1 Add '-1lnx' to each side of the equation. lnx + -1lnx = -1 + -1lnx Combine like terms: lnx + -1lnx = 0 0 = -1 + -1lnx Simplifying 0 = -1 + -1lnx 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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