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Simplifying y(x3 + xy2 + -1y) * dx + (y3 + x2y + x) * dy = 0 Reorder the terms: y(xy2 + x3 + -1y) * dx + (y3 + x2y + x) * dy = 0 Reorder the terms for easier multiplication: y * dx(xy2 + x3 + -1y) + (y3 + x2y + x) * dy = 0 Multiply y * dx dxy(xy2 + x3 + -1y) + (y3 + x2y + x) * dy = 0 (xy2 * dxy + x3 * dxy + -1y * dxy) + (y3 + x2y + x) * dy = 0 Reorder the terms: (-1dxy2 + dx2y3 + dx4y) + (y3 + x2y + x) * dy = 0 (-1dxy2 + dx2y3 + dx4y) + (y3 + x2y + x) * dy = 0 Reorder the terms: -1dxy2 + dx2y3 + dx4y + (x + x2y + y3) * dy = 0 Reorder the terms for easier multiplication: -1dxy2 + dx2y3 + dx4y + dy(x + x2y + y3) = 0 -1dxy2 + dx2y3 + dx4y + (x * dy + x2y * dy + y3 * dy) = 0 -1dxy2 + dx2y3 + dx4y + (dxy + dx2y2 + dy4) = 0 Reorder the terms: dxy + -1dxy2 + dx2y2 + dx2y3 + dx4y + dy4 = 0 Solving dxy + -1dxy2 + dx2y2 + dx2y3 + dx4y + dy4 = 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 + -1xy + x2y + x2y2 + x4 + y3) = 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 + -1xy + x2y + x2y2 + x4 + y3)' equal to zero and attempt to solve: Simplifying x + -1xy + x2y + x2y2 + x4 + y3 = 0 Solving x + -1xy + x2y + x2y2 + x4 + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1xy + x2y + x2y2 + x4 + -1x + y3 = 0 + -1x Reorder the terms: x + -1x + -1xy + x2y + x2y2 + x4 + y3 = 0 + -1x Combine like terms: x + -1x = 0 0 + -1xy + x2y + x2y2 + x4 + y3 = 0 + -1x -1xy + x2y + x2y2 + x4 + y3 = 0 + -1x Remove the zero: -1xy + x2y + x2y2 + x4 + y3 = -1x Add 'xy' to each side of the equation. -1xy + x2y + x2y2 + x4 + xy + y3 = -1x + xy Reorder the terms: -1xy + xy + x2y + x2y2 + x4 + y3 = -1x + xy Combine like terms: -1xy + xy = 0 0 + x2y + x2y2 + x4 + y3 = -1x + xy x2y + x2y2 + x4 + y3 = -1x + xy Add '-1x2y' to each side of the equation. x2y + x2y2 + x4 + -1x2y + y3 = -1x + xy + -1x2y Reorder the terms: x2y + -1x2y + x2y2 + x4 + y3 = -1x + xy + -1x2y Combine like terms: x2y + -1x2y = 0 0 + x2y2 + x4 + y3 = -1x + xy + -1x2y x2y2 + x4 + y3 = -1x + xy + -1x2y Add '-1x2y2' to each side of the equation. x2y2 + x4 + -1x2y2 + y3 = -1x + xy + -1x2y + -1x2y2 Reorder the terms: x2y2 + -1x2y2 + x4 + y3 = -1x + xy + -1x2y + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + x4 + y3 = -1x + xy + -1x2y + -1x2y2 x4 + y3 = -1x + xy + -1x2y + -1x2y2 Add '-1x4' to each side of the equation. x4 + -1x4 + y3 = -1x + xy + -1x2y + -1x2y2 + -1x4 Combine like terms: x4 + -1x4 = 0 0 + y3 = -1x + xy + -1x2y + -1x2y2 + -1x4 y3 = -1x + xy + -1x2y + -1x2y2 + -1x4 Add '-1y3' to each side of the equation. y3 + -1y3 = -1x + xy + -1x2y + -1x2y2 + -1x4 + -1y3 Combine like terms: y3 + -1y3 = 0 0 = -1x + xy + -1x2y + -1x2y2 + -1x4 + -1y3 Simplifying 0 = -1x + xy + -1x2y + -1x2y2 + -1x4 + -1y3 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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