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Simplifying (x2 + y2) * dy = (2xy) * dx Reorder the terms for easier multiplication: dy(x2 + y2) = (2xy) * dx (x2 * dy + y2 * dy) = (2xy) * dx (dx2y + dy3) = (2xy) * dx Remove parenthesis around (2xy) dx2y + dy3 = 2xy * dx Multiply xy * dx dx2y + dy3 = 2dx2y Solving dx2y + dy3 = 2dx2y Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dx2y' to each side of the equation. dx2y + -2dx2y + dy3 = 2dx2y + -2dx2y Combine like terms: dx2y + -2dx2y = -1dx2y -1dx2y + dy3 = 2dx2y + -2dx2y Combine like terms: 2dx2y + -2dx2y = 0 -1dx2y + dy3 = 0 Factor out the Greatest Common Factor (GCF), 'dy'. dy(-1x2 + y2) = 0 Factor a difference between two squares. dy((x + y)(-1x + 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 '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1x + y)' equal to zero and attempt to solve: Simplifying -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -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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