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Simplifying x(ln(y) + 2ln(x) + -1) * dy = 2ydx Multiply ln * y x(lny + 2ln(x) + -1) * dy = 2ydx Multiply ln * x x(lny + 2lnx + -1) * dy = 2ydx Reorder the terms: x(-1 + 2lnx + lny) * dy = 2ydx Reorder the terms for easier multiplication: x * dy(-1 + 2lnx + lny) = 2ydx Multiply x * dy dxy(-1 + 2lnx + lny) = 2ydx (-1 * dxy + 2lnx * dxy + lny * dxy) = 2ydx Reorder the terms: (dlnxy2 + 2dlnx2y + -1dxy) = 2ydx (dlnxy2 + 2dlnx2y + -1dxy) = 2ydx Solving dlnxy2 + 2dlnx2y + -1dxy = 2dxy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dxy' to each side of the equation. dlnxy2 + 2dlnx2y + -1dxy + -2dxy = 2dxy + -2dxy Combine like terms: -1dxy + -2dxy = -3dxy dlnxy2 + 2dlnx2y + -3dxy = 2dxy + -2dxy Combine like terms: 2dxy + -2dxy = 0 dlnxy2 + 2dlnx2y + -3dxy = 0 Factor out the Greatest Common Factor (GCF), 'dxy'. dxy(lny + 2lnx + -3) = 0Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(lny + 2lnx + -3)' equal to zero and attempt to solve: Simplifying lny + 2lnx + -3 = 0 Reorder the terms: -3 + 2lnx + lny = 0 Solving -3 + 2lnx + lny = 0 Move all terms containing d to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 2lnx + 3 + lny = 0 + 3 Reorder the terms: -3 + 3 + 2lnx + lny = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2lnx + lny = 0 + 3 2lnx + lny = 0 + 3 Combine like terms: 0 + 3 = 3 2lnx + lny = 3 Add '-2lnx' to each side of the equation. 2lnx + -2lnx + lny = 3 + -2lnx Combine like terms: 2lnx + -2lnx = 0 0 + lny = 3 + -2lnx lny = 3 + -2lnx Add '-1lny' to each side of the equation. lny + -1lny = 3 + -2lnx + -1lny Combine like terms: lny + -1lny = 0 0 = 3 + -2lnx + -1lny Simplifying 0 = 3 + -2lnx + -1lny 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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