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