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Simplifying (xy + y2) * dx + (x + 2y) * dy = 0 Reorder the terms for easier multiplication: dx(xy + y2) + (x + 2y) * dy = 0 (xy * dx + y2 * dx) + (x + 2y) * dy = 0 Reorder the terms: (dxy2 + dx2y) + (x + 2y) * dy = 0 (dxy2 + dx2y) + (x + 2y) * dy = 0 Reorder the terms for easier multiplication: dxy2 + dx2y + dy(x + 2y) = 0 dxy2 + dx2y + (x * dy + 2y * dy) = 0 dxy2 + dx2y + (dxy + 2dy2) = 0 Reorder the terms: dxy + dxy2 + dx2y + 2dy2 = 0 Solving dxy + dxy2 + dx2y + 2dy2 = 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(x + xy + x2 + 2y) = 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 '(x + xy + x2 + 2y)' equal to zero and attempt to solve: Simplifying x + xy + x2 + 2y = 0 Solving x + xy + x2 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + xy + x2 + -1x + 2y = 0 + -1x Reorder the terms: x + -1x + xy + x2 + 2y = 0 + -1x Combine like terms: x + -1x = 0 0 + xy + x2 + 2y = 0 + -1x xy + x2 + 2y = 0 + -1x Remove the zero: xy + x2 + 2y = -1x Add '-1xy' to each side of the equation. xy + x2 + -1xy + 2y = -1x + -1xy Reorder the terms: xy + -1xy + x2 + 2y = -1x + -1xy Combine like terms: xy + -1xy = 0 0 + x2 + 2y = -1x + -1xy x2 + 2y = -1x + -1xy Add '-1x2' to each side of the equation. x2 + -1x2 + 2y = -1x + -1xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y = -1x + -1xy + -1x2 2y = -1x + -1xy + -1x2 Add '-2y' to each side of the equation. 2y + -2y = -1x + -1xy + -1x2 + -2y Combine like terms: 2y + -2y = 0 0 = -1x + -1xy + -1x2 + -2y Simplifying 0 = -1x + -1xy + -1x2 + -2y 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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