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Simplifying y(2x + y) * dx + (3x2 + 4xy + -1y) * dy = 0 Reorder the terms for easier multiplication: y * dx(2x + y) + (3x2 + 4xy + -1y) * dy = 0 Multiply y * dx dxy(2x + y) + (3x2 + 4xy + -1y) * dy = 0 (2x * dxy + y * dxy) + (3x2 + 4xy + -1y) * dy = 0 Reorder the terms: (dxy2 + 2dx2y) + (3x2 + 4xy + -1y) * dy = 0 (dxy2 + 2dx2y) + (3x2 + 4xy + -1y) * dy = 0 Reorder the terms: dxy2 + 2dx2y + (4xy + 3x2 + -1y) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 2dx2y + dy(4xy + 3x2 + -1y) = 0 dxy2 + 2dx2y + (4xy * dy + 3x2 * dy + -1y * dy) = 0 dxy2 + 2dx2y + (4dxy2 + 3dx2y + -1dy2) = 0 Reorder the terms: dxy2 + 4dxy2 + 2dx2y + 3dx2y + -1dy2 = 0 Combine like terms: dxy2 + 4dxy2 = 5dxy2 5dxy2 + 2dx2y + 3dx2y + -1dy2 = 0 Combine like terms: 2dx2y + 3dx2y = 5dx2y 5dxy2 + 5dx2y + -1dy2 = 0 Solving 5dxy2 + 5dx2y + -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(5xy + 5x2 + -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 '(5xy + 5x2 + -1y)' equal to zero and attempt to solve: Simplifying 5xy + 5x2 + -1y = 0 Solving 5xy + 5x2 + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-5xy' to each side of the equation. 5xy + 5x2 + -5xy + -1y = 0 + -5xy Reorder the terms: 5xy + -5xy + 5x2 + -1y = 0 + -5xy Combine like terms: 5xy + -5xy = 0 0 + 5x2 + -1y = 0 + -5xy 5x2 + -1y = 0 + -5xy Remove the zero: 5x2 + -1y = -5xy Add '-5x2' to each side of the equation. 5x2 + -5x2 + -1y = -5xy + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 + -1y = -5xy + -5x2 -1y = -5xy + -5x2 Add 'y' to each side of the equation. -1y + y = -5xy + -5x2 + y Combine like terms: -1y + y = 0 0 = -5xy + -5x2 + y Simplifying 0 = -5xy + -5x2 + 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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