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Simplifying ydx + x(y2 + lnx) * dy = 0 Reorder the terms: dxy + x(lnx + y2) * dy = 0 Reorder the terms for easier multiplication: dxy + x * dy(lnx + y2) = 0 Multiply x * dy dxy + dxy(lnx + y2) = 0 dxy + (lnx * dxy + y2 * dxy) = 0 dxy + (dlnx2y + dxy3) = 0 Reorder the terms: dlnx2y + dxy + dxy3 = 0 Solving dlnx2y + dxy + dxy3 = 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), 'dxy'. dxy(lnx + 1 + y2) = 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 '(lnx + 1 + y2)' equal to zero and attempt to solve: Simplifying lnx + 1 + y2 = 0 Reorder the terms: 1 + lnx + y2 = 0 Solving 1 + lnx + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + lnx + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + lnx + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + lnx + y2 = 0 + -1 lnx + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 lnx + y2 = -1 Add '-1lnx' to each side of the equation. lnx + -1lnx + y2 = -1 + -1lnx Combine like terms: lnx + -1lnx = 0 0 + y2 = -1 + -1lnx y2 = -1 + -1lnx Add '-1y2' to each side of the equation. y2 + -1y2 = -1 + -1lnx + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1 + -1lnx + -1y2 Simplifying 0 = -1 + -1lnx + -1y2 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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