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Simplifying (2xy + y) * dx + (x2 + -1y) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + y) + (x2 + -1y) * dy = 0 (2xy * dx + y * dx) + (x2 + -1y) * dy = 0 Reorder the terms: (dxy + 2dx2y) + (x2 + -1y) * dy = 0 (dxy + 2dx2y) + (x2 + -1y) * dy = 0 Reorder the terms for easier multiplication: dxy + 2dx2y + dy(x2 + -1y) = 0 dxy + 2dx2y + (x2 * dy + -1y * dy) = 0 dxy + 2dx2y + (dx2y + -1dy2) = 0 Combine like terms: 2dx2y + dx2y = 3dx2y dxy + 3dx2y + -1dy2 = 0 Solving dxy + 3dx2y + -1dy2 = 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), 'dy'. dy(x + 3x2 + -1y) = 0Subproblem 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 '(x + 3x2 + -1y)' equal to zero and attempt to solve: Simplifying x + 3x2 + -1y = 0 Solving x + 3x2 + -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 + 3x2 + -1x + -1y = 0 + -1x Reorder the terms: x + -1x + 3x2 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + 3x2 + -1y = 0 + -1x 3x2 + -1y = 0 + -1x Remove the zero: 3x2 + -1y = -1x Add '-3x2' to each side of the equation. 3x2 + -3x2 + -1y = -1x + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -1y = -1x + -3x2 -1y = -1x + -3x2 Add 'y' to each side of the equation. -1y + y = -1x + -3x2 + y Combine like terms: -1y + y = 0 0 = -1x + -3x2 + y Simplifying 0 = -1x + -3x2 + 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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