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Simplifying y(x + y + 1) * dx + x(x + 3y + 2) * dy = 0 Reorder the terms: y(1 + x + y) * dx + x(x + 3y + 2) * dy = 0 Reorder the terms for easier multiplication: y * dx(1 + x + y) + x(x + 3y + 2) * dy = 0 Multiply y * dx dxy(1 + x + y) + x(x + 3y + 2) * dy = 0 (1 * dxy + x * dxy + y * dxy) + x(x + 3y + 2) * dy = 0 Reorder the terms: (1dxy + dxy2 + dx2y) + x(x + 3y + 2) * dy = 0 (1dxy + dxy2 + dx2y) + x(x + 3y + 2) * dy = 0 Reorder the terms: 1dxy + dxy2 + dx2y + x(2 + x + 3y) * dy = 0 Reorder the terms for easier multiplication: 1dxy + dxy2 + dx2y + x * dy(2 + x + 3y) = 0 Multiply x * dy 1dxy + dxy2 + dx2y + dxy(2 + x + 3y) = 0 1dxy + dxy2 + dx2y + (2 * dxy + x * dxy + 3y * dxy) = 0 Reorder the terms: 1dxy + dxy2 + dx2y + (2dxy + 3dxy2 + dx2y) = 0 1dxy + dxy2 + dx2y + (2dxy + 3dxy2 + dx2y) = 0 Reorder the terms: 1dxy + 2dxy + dxy2 + 3dxy2 + dx2y + dx2y = 0 Combine like terms: 1dxy + 2dxy = 3dxy 3dxy + dxy2 + 3dxy2 + dx2y + dx2y = 0 Combine like terms: dxy2 + 3dxy2 = 4dxy2 3dxy + 4dxy2 + dx2y + dx2y = 0 Combine like terms: dx2y + dx2y = 2dx2y 3dxy + 4dxy2 + 2dx2y = 0 Solving 3dxy + 4dxy2 + 2dx2y = 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), 'dxy'. dxy(3 + 4y + 2x) = 0Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(3 + 4y + 2x)' equal to zero and attempt to solve: Simplifying 3 + 4y + 2x = 0 Reorder the terms: 3 + 2x + 4y = 0 Solving 3 + 2x + 4y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 2x + -3 + 4y = 0 + -3 Reorder the terms: 3 + -3 + 2x + 4y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x + 4y = 0 + -3 2x + 4y = 0 + -3 Combine like terms: 0 + -3 = -3 2x + 4y = -3 Add '-2x' to each side of the equation. 2x + -2x + 4y = -3 + -2x Combine like terms: 2x + -2x = 0 0 + 4y = -3 + -2x 4y = -3 + -2x Add '-4y' to each side of the equation. 4y + -4y = -3 + -2x + -4y Combine like terms: 4y + -4y = 0 0 = -3 + -2x + -4y Simplifying 0 = -3 + -2x + -4y 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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