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Simplifying dx + (x + y + 1) * dy = 0 Reorder the terms: dx + (1 + x + y) * dy = 0 Reorder the terms for easier multiplication: dx + dy(1 + x + y) = 0 dx + (1 * dy + x * dy + y * dy) = 0 Reorder the terms: dx + (dxy + 1dy + dy2) = 0 dx + (dxy + 1dy + dy2) = 0 Solving dx + dxy + 1dy + 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), 'd'. d(x + xy + y + y2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(x + xy + y + y2)' equal to zero and attempt to solve: Simplifying x + xy + y + y2 = 0 Solving x + xy + y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + xy + y + -1x + y2 = 0 + -1x Reorder the terms: x + -1x + xy + y + y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + xy + y + y2 = 0 + -1x xy + y + y2 = 0 + -1x Remove the zero: xy + y + y2 = -1x Add '-1xy' to each side of the equation. xy + y + -1xy + y2 = -1x + -1xy Reorder the terms: xy + -1xy + y + y2 = -1x + -1xy Combine like terms: xy + -1xy = 0 0 + y + y2 = -1x + -1xy y + y2 = -1x + -1xy Add '-1y' to each side of the equation. y + -1y + y2 = -1x + -1xy + -1y Combine like terms: y + -1y = 0 0 + y2 = -1x + -1xy + -1y y2 = -1x + -1xy + -1y Add '-1y2' to each side of the equation. y2 + -1y2 = -1x + -1xy + -1y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x + -1xy + -1y + -1y2 Simplifying 0 = -1x + -1xy + -1y + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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