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Simplifying 2y(x + y + 2) * dx + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms: 2y(2 + x + y) * dx + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms for easier multiplication: 2y * dx(2 + x + y) + (y2 + -1x2 + -4x + -1) * dy = 0 Multiply y * dx 2dxy(2 + x + y) + (y2 + -1x2 + -4x + -1) * dy = 0 (2 * 2dxy + x * 2dxy + y * 2dxy) + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms: (4dxy + 2dxy2 + 2dx2y) + (y2 + -1x2 + -4x + -1) * dy = 0 (4dxy + 2dxy2 + 2dx2y) + (y2 + -1x2 + -4x + -1) * dy = 0 Reorder the terms: 4dxy + 2dxy2 + 2dx2y + (-1 + -4x + -1x2 + y2) * dy = 0 Reorder the terms for easier multiplication: 4dxy + 2dxy2 + 2dx2y + dy(-1 + -4x + -1x2 + y2) = 0 4dxy + 2dxy2 + 2dx2y + (-1 * dy + -4x * dy + -1x2 * dy + y2 * dy) = 0 Reorder the terms: 4dxy + 2dxy2 + 2dx2y + (-4dxy + -1dx2y + -1dy + dy3) = 0 4dxy + 2dxy2 + 2dx2y + (-4dxy + -1dx2y + -1dy + dy3) = 0 Reorder the terms: 4dxy + -4dxy + 2dxy2 + 2dx2y + -1dx2y + -1dy + dy3 = 0 Combine like terms: 4dxy + -4dxy = 0 0 + 2dxy2 + 2dx2y + -1dx2y + -1dy + dy3 = 0 2dxy2 + 2dx2y + -1dx2y + -1dy + dy3 = 0 Combine like terms: 2dx2y + -1dx2y = 1dx2y 2dxy2 + 1dx2y + -1dy + dy3 = 0 Solving 2dxy2 + 1dx2y + -1dy + dy3 = 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(2xy + x2 + -1 + y2) = 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 '(2xy + x2 + -1 + y2)' equal to zero and attempt to solve: Simplifying 2xy + x2 + -1 + y2 = 0 Reorder the terms: -1 + 2xy + x2 + y2 = 0 Solving -1 + 2xy + x2 + 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 + 2xy + x2 + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 2xy + x2 + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2xy + x2 + y2 = 0 + 1 2xy + x2 + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 2xy + x2 + y2 = 1 Add '-2xy' to each side of the equation. 2xy + x2 + -2xy + y2 = 1 + -2xy Reorder the terms: 2xy + -2xy + x2 + y2 = 1 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + y2 = 1 + -2xy x2 + y2 = 1 + -2xy Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 1 + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 1 + -2xy + -1x2 y2 = 1 + -2xy + -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = 1 + -2xy + -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 1 + -2xy + -1x2 + -1y2 Simplifying 0 = 1 + -2xy + -1x2 + -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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