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