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Simplifying (1 + x4) * dy + x(1 + 4y2) * dx = 0 Reorder the terms for easier multiplication: dy(1 + x4) + x(1 + 4y2) * dx = 0 (1 * dy + x4 * dy) + x(1 + 4y2) * dx = 0 Reorder the terms: (dx4y + 1dy) + x(1 + 4y2) * dx = 0 (dx4y + 1dy) + x(1 + 4y2) * dx = 0 Reorder the terms for easier multiplication: dx4y + 1dy + x * dx(1 + 4y2) = 0 Multiply x * dx dx4y + 1dy + dx2(1 + 4y2) = 0 dx4y + 1dy + (1 * dx2 + 4y2 * dx2) = 0 dx4y + 1dy + (1dx2 + 4dx2y2) = 0 Reorder the terms: 1dx2 + 4dx2y2 + dx4y + 1dy = 0 Solving 1dx2 + 4dx2y2 + dx4y + 1dy = 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(x2 + 4x2y2 + x4y + y) = 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 '(x2 + 4x2y2 + x4y + y)' equal to zero and attempt to solve: Simplifying x2 + 4x2y2 + x4y + y = 0 Solving x2 + 4x2y2 + x4y + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + 4x2y2 + x4y + -1x2 + y = 0 + -1x2 Reorder the terms: x2 + -1x2 + 4x2y2 + x4y + y = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 4x2y2 + x4y + y = 0 + -1x2 4x2y2 + x4y + y = 0 + -1x2 Remove the zero: 4x2y2 + x4y + y = -1x2 Add '-4x2y2' to each side of the equation. 4x2y2 + x4y + -4x2y2 + y = -1x2 + -4x2y2 Reorder the terms: 4x2y2 + -4x2y2 + x4y + y = -1x2 + -4x2y2 Combine like terms: 4x2y2 + -4x2y2 = 0 0 + x4y + y = -1x2 + -4x2y2 x4y + y = -1x2 + -4x2y2 Add '-1x4y' to each side of the equation. x4y + -1x4y + y = -1x2 + -4x2y2 + -1x4y Combine like terms: x4y + -1x4y = 0 0 + y = -1x2 + -4x2y2 + -1x4y y = -1x2 + -4x2y2 + -1x4y Add '-1y' to each side of the equation. y + -1y = -1x2 + -4x2y2 + -1x4y + -1y Combine like terms: y + -1y = 0 0 = -1x2 + -4x2y2 + -1x4y + -1y Simplifying 0 = -1x2 + -4x2y2 + -1x4y + -1y 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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