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Simplifying 3y(x2 + -1) * dx + (x3 + 8y + 3x) * dy = 0 Reorder the terms: 3y(-1 + x2) * dx + (x3 + 8y + 3x) * dy = 0 Reorder the terms for easier multiplication: 3y * dx(-1 + x2) + (x3 + 8y + 3x) * dy = 0 Multiply y * dx 3dxy(-1 + x2) + (x3 + 8y + 3x) * dy = 0 (-1 * 3dxy + x2 * 3dxy) + (x3 + 8y + 3x) * dy = 0 (-3dxy + 3dx3y) + (x3 + 8y + 3x) * dy = 0 Reorder the terms: -3dxy + 3dx3y + (3x + x3 + 8y) * dy = 0 Reorder the terms for easier multiplication: -3dxy + 3dx3y + dy(3x + x3 + 8y) = 0 -3dxy + 3dx3y + (3x * dy + x3 * dy + 8y * dy) = 0 -3dxy + 3dx3y + (3dxy + dx3y + 8dy2) = 0 Reorder the terms: -3dxy + 3dxy + 3dx3y + dx3y + 8dy2 = 0 Combine like terms: -3dxy + 3dxy = 0 0 + 3dx3y + dx3y + 8dy2 = 0 3dx3y + dx3y + 8dy2 = 0 Combine like terms: 3dx3y + dx3y = 4dx3y 4dx3y + 8dy2 = 0 Solving 4dx3y + 8dy2 = 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), '4dy'. 4dy(x3 + 2y) = 0 Ignore the factor 4.Subproblem 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 '(x3 + 2y)' equal to zero and attempt to solve: Simplifying x3 + 2y = 0 Solving x3 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x3' to each side of the equation. x3 + -1x3 + 2y = 0 + -1x3 Combine like terms: x3 + -1x3 = 0 0 + 2y = 0 + -1x3 2y = 0 + -1x3 Remove the zero: 2y = -1x3 Add '-2y' to each side of the equation. 2y + -2y = -1x3 + -2y Combine like terms: 2y + -2y = 0 0 = -1x3 + -2y Simplifying 0 = -1x3 + -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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