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Simplifying y(x2 + y2) * dx + x(3x2 + -5y2) * dy = 0 Reorder the terms for easier multiplication: y * dx(x2 + y2) + x(3x2 + -5y2) * dy = 0 Multiply y * dx dxy(x2 + y2) + x(3x2 + -5y2) * dy = 0 (x2 * dxy + y2 * dxy) + x(3x2 + -5y2) * dy = 0 Reorder the terms: (dxy3 + dx3y) + x(3x2 + -5y2) * dy = 0 (dxy3 + dx3y) + x(3x2 + -5y2) * dy = 0 Reorder the terms for easier multiplication: dxy3 + dx3y + x * dy(3x2 + -5y2) = 0 Multiply x * dy dxy3 + dx3y + dxy(3x2 + -5y2) = 0 dxy3 + dx3y + (3x2 * dxy + -5y2 * dxy) = 0 Reorder the terms: dxy3 + dx3y + (-5dxy3 + 3dx3y) = 0 dxy3 + dx3y + (-5dxy3 + 3dx3y) = 0 Reorder the terms: dxy3 + -5dxy3 + dx3y + 3dx3y = 0 Combine like terms: dxy3 + -5dxy3 = -4dxy3 -4dxy3 + dx3y + 3dx3y = 0 Combine like terms: dx3y + 3dx3y = 4dx3y -4dxy3 + 4dx3y = 0 Solving -4dxy3 + 4dx3y = 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), '4dxy'. 4dxy(-1y2 + x2) = 0 Factor a difference between two squares. 4dxy((y + x)(-1y + x)) = 0 Ignore the factor 4.Subproblem 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 '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1y + x)' equal to zero and attempt to solve: Simplifying -1y + x = 0 Reorder the terms: x + -1y = 0 Solving x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y 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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