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Simplifying 2ydx + (x + 4y2) * dy = 0 Reorder the terms for easier multiplication: 2dxy + dy(x + 4y2) = 0 2dxy + (x * dy + 4y2 * dy) = 0 2dxy + (dxy + 4dy3) = 0 Combine like terms: 2dxy + dxy = 3dxy 3dxy + 4dy3 = 0 Solving 3dxy + 4dy3 = 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(3x + 4y2) = 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 '(3x + 4y2)' equal to zero and attempt to solve: Simplifying 3x + 4y2 = 0 Solving 3x + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + -3x + 4y2 = 0 + -3x Combine like terms: 3x + -3x = 0 0 + 4y2 = 0 + -3x 4y2 = 0 + -3x Remove the zero: 4y2 = -3x Add '-4y2' to each side of the equation. 4y2 + -4y2 = -3x + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -3x + -4y2 Simplifying 0 = -3x + -4y2 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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