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Simplifying (y2 + 1) * dy + (2xy + 1) * dx = 0 Reorder the terms: (1 + y2) * dy + (2xy + 1) * dx = 0 Reorder the terms for easier multiplication: dy(1 + y2) + (2xy + 1) * dx = 0 (1 * dy + y2 * dy) + (2xy + 1) * dx = 0 (1dy + dy3) + (2xy + 1) * dx = 0 Reorder the terms: 1dy + dy3 + (1 + 2xy) * dx = 0 Reorder the terms for easier multiplication: 1dy + dy3 + dx(1 + 2xy) = 0 1dy + dy3 + (1 * dx + 2xy * dx) = 0 1dy + dy3 + (1dx + 2dx2y) = 0 Reorder the terms: 1dx + 2dx2y + 1dy + dy3 = 0 Solving 1dx + 2dx2y + 1dy + dy3 = 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 + 2x2y + y + y3) = 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 + 2x2y + y + y3)' equal to zero and attempt to solve: Simplifying x + 2x2y + y + y3 = 0 Solving x + 2x2y + y + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 2x2y + y + -1x + y3 = 0 + -1x Reorder the terms: x + -1x + 2x2y + y + y3 = 0 + -1x Combine like terms: x + -1x = 0 0 + 2x2y + y + y3 = 0 + -1x 2x2y + y + y3 = 0 + -1x Remove the zero: 2x2y + y + y3 = -1x Add '-2x2y' to each side of the equation. 2x2y + y + -2x2y + y3 = -1x + -2x2y Reorder the terms: 2x2y + -2x2y + y + y3 = -1x + -2x2y Combine like terms: 2x2y + -2x2y = 0 0 + y + y3 = -1x + -2x2y y + y3 = -1x + -2x2y Add '-1y' to each side of the equation. y + -1y + y3 = -1x + -2x2y + -1y Combine like terms: y + -1y = 0 0 + y3 = -1x + -2x2y + -1y y3 = -1x + -2x2y + -1y Add '-1y3' to each side of the equation. y3 + -1y3 = -1x + -2x2y + -1y + -1y3 Combine like terms: y3 + -1y3 = 0 0 = -1x + -2x2y + -1y + -1y3 Simplifying 0 = -1x + -2x2y + -1y + -1y3 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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