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Simplifying xdy + -1y + xy3(1 + lnx) * dx = 0 Reorder the terms for easier multiplication: dxy + -1y + xy3 * dx(1 + lnx) = 0 Multiply xy3 * dx dxy + -1y + dx2y3(1 + lnx) = 0 dxy + -1y + (1 * dx2y3 + lnx * dx2y3) = 0 Reorder the terms: dxy + -1y + (dlnx3y3 + 1dx2y3) = 0 dxy + -1y + (dlnx3y3 + 1dx2y3) = 0 Reorder the terms: dlnx3y3 + dxy + 1dx2y3 + -1y = 0 Solving dlnx3y3 + dxy + 1dx2y3 + -1y = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add 'y' to each side of the equation. dlnx3y3 + dxy + 1dx2y3 + -1y + y = 0 + y Combine like terms: -1y + y = 0 dlnx3y3 + dxy + 1dx2y3 + 0 = 0 + y dlnx3y3 + dxy + 1dx2y3 = 0 + y Remove the zero: dlnx3y3 + dxy + 1dx2y3 = y Combine like terms: y + -1y = 0 dlnx3y3 + dxy + 1dx2y3 + -1y = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(dlnx3y2 + dx + dx2y2 + -1) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y 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 '(dlnx3y2 + dx + dx2y2 + -1)' equal to zero and attempt to solve: Simplifying dlnx3y2 + dx + dx2y2 + -1 = 0 Reorder the terms: -1 + dlnx3y2 + dx + dx2y2 = 0 Solving -1 + dlnx3y2 + dx + dx2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + dlnx3y2 + dx + 1 + dx2y2 = 0 + 1 Reorder the terms: -1 + 1 + dlnx3y2 + dx + dx2y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + dlnx3y2 + dx + dx2y2 = 0 + 1 dlnx3y2 + dx + dx2y2 = 0 + 1 Combine like terms: 0 + 1 = 1 dlnx3y2 + dx + dx2y2 = 1 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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