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Simplifying (2x2y + x) * dy + (xy2 + y) * dx = 0 Reorder the terms: (x + 2x2y) * dy + (xy2 + y) * dx = 0 Reorder the terms for easier multiplication: dy(x + 2x2y) + (xy2 + y) * dx = 0 (x * dy + 2x2y * dy) + (xy2 + y) * dx = 0 (dxy + 2dx2y2) + (xy2 + y) * dx = 0 Reorder the terms for easier multiplication: dxy + 2dx2y2 + dx(xy2 + y) = 0 dxy + 2dx2y2 + (xy2 * dx + y * dx) = 0 Reorder the terms: dxy + 2dx2y2 + (dxy + dx2y2) = 0 dxy + 2dx2y2 + (dxy + dx2y2) = 0 Reorder the terms: dxy + dxy + 2dx2y2 + dx2y2 = 0 Combine like terms: dxy + dxy = 2dxy 2dxy + 2dx2y2 + dx2y2 = 0 Combine like terms: 2dx2y2 + dx2y2 = 3dx2y2 2dxy + 3dx2y2 = 0 Solving 2dxy + 3dx2y2 = 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(2 + 3xy) = 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 '(2 + 3xy)' equal to zero and attempt to solve: Simplifying 2 + 3xy = 0 Solving 2 + 3xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3xy = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3xy = 0 + -2 3xy = 0 + -2 Combine like terms: 0 + -2 = -2 3xy = -2 Add '-3xy' to each side of the equation. 3xy + -3xy = -2 + -3xy Combine like terms: 3xy + -3xy = 0 0 = -2 + -3xy Simplifying 0 = -2 + -3xy 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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