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Simplifying (y2 + 9x) * dy = 6ydx Reorder the terms: (9x + y2) * dy = 6ydx Reorder the terms for easier multiplication: dy(9x + y2) = 6ydx (9x * dy + y2 * dy) = 6ydx (9dxy + dy3) = 6ydx Solving 9dxy + dy3 = 6dxy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6dxy' to each side of the equation. 9dxy + -6dxy + dy3 = 6dxy + -6dxy Combine like terms: 9dxy + -6dxy = 3dxy 3dxy + dy3 = 6dxy + -6dxy Combine like terms: 6dxy + -6dxy = 0 3dxy + dy3 = 0 Factor out the Greatest Common Factor (GCF), 'dy'. dy(3x + y2) = 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 + y2)' equal to zero and attempt to solve: Simplifying 3x + y2 = 0 Solving 3x + y2 = 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 + y2 = 0 + -3x Combine like terms: 3x + -3x = 0 0 + y2 = 0 + -3x y2 = 0 + -3x Remove the zero: y2 = -3x Add '-1y2' to each side of the equation. y2 + -1y2 = -3x + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -3x + -1y2 Simplifying 0 = -3x + -1y2 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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