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Simplifying (3x2y + y3) * dx + (x3 + 3xy2) * dy = 0 Reorder the terms for easier multiplication: dx(3x2y + y3) + (x3 + 3xy2) * dy = 0 (3x2y * dx + y3 * dx) + (x3 + 3xy2) * dy = 0 Reorder the terms: (dxy3 + 3dx3y) + (x3 + 3xy2) * dy = 0 (dxy3 + 3dx3y) + (x3 + 3xy2) * dy = 0 Reorder the terms: dxy3 + 3dx3y + (3xy2 + x3) * dy = 0 Reorder the terms for easier multiplication: dxy3 + 3dx3y + dy(3xy2 + x3) = 0 dxy3 + 3dx3y + (3xy2 * dy + x3 * dy) = 0 dxy3 + 3dx3y + (3dxy3 + dx3y) = 0 Reorder the terms: dxy3 + 3dxy3 + 3dx3y + dx3y = 0 Combine like terms: dxy3 + 3dxy3 = 4dxy3 4dxy3 + 3dx3y + dx3y = 0 Combine like terms: 3dx3y + dx3y = 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(y2 + x2) = 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 '(y2 + x2)' equal to zero and attempt to solve: Simplifying y2 + x2 = 0 Reorder the terms: x2 + y2 = 0 Solving x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 0 + -1x2 y2 = 0 + -1x2 Remove the zero: y2 = -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x2 + -1y2 Simplifying 0 = -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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