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Simplifying (5x * y2 + -1x3) * dx + (5x2 * y + -1y) * dy = 0 Multiply x * y2 (5xy2 + -1x3) * dx + (5x2 * y + -1y) * dy = 0 Reorder the terms for easier multiplication: dx(5xy2 + -1x3) + (5x2 * y + -1y) * dy = 0 (5xy2 * dx + -1x3 * dx) + (5x2 * y + -1y) * dy = 0 (5dx2y2 + -1dx4) + (5x2 * y + -1y) * dy = 0 Multiply x2 * y 5dx2y2 + -1dx4 + (5x2y + -1y) * dy = 0 Reorder the terms for easier multiplication: 5dx2y2 + -1dx4 + dy(5x2y + -1y) = 0 5dx2y2 + -1dx4 + (5x2y * dy + -1y * dy) = 0 5dx2y2 + -1dx4 + (5dx2y2 + -1dy2) = 0 Reorder the terms: 5dx2y2 + 5dx2y2 + -1dx4 + -1dy2 = 0 Combine like terms: 5dx2y2 + 5dx2y2 = 10dx2y2 10dx2y2 + -1dx4 + -1dy2 = 0 Solving 10dx2y2 + -1dx4 + -1dy2 = 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(10x2y2 + -1x4 + -1y2) = 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 '(10x2y2 + -1x4 + -1y2)' equal to zero and attempt to solve: Simplifying 10x2y2 + -1x4 + -1y2 = 0 Solving 10x2y2 + -1x4 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-10x2y2' to each side of the equation. 10x2y2 + -1x4 + -10x2y2 + -1y2 = 0 + -10x2y2 Reorder the terms: 10x2y2 + -10x2y2 + -1x4 + -1y2 = 0 + -10x2y2 Combine like terms: 10x2y2 + -10x2y2 = 0 0 + -1x4 + -1y2 = 0 + -10x2y2 -1x4 + -1y2 = 0 + -10x2y2 Remove the zero: -1x4 + -1y2 = -10x2y2 Add 'x4' to each side of the equation. -1x4 + x4 + -1y2 = -10x2y2 + x4 Combine like terms: -1x4 + x4 = 0 0 + -1y2 = -10x2y2 + x4 -1y2 = -10x2y2 + x4 Add 'y2' to each side of the equation. -1y2 + y2 = -10x2y2 + x4 + y2 Combine like terms: -1y2 + y2 = 0 0 = -10x2y2 + x4 + y2 Simplifying 0 = -10x2y2 + x4 + y2 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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