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Simplifying y2dx + (xy + 2y3) * dy = 0 Reorder the terms for easier multiplication: dxy2 + dy(xy + 2y3) = 0 dxy2 + (xy * dy + 2y3 * dy) = 0 dxy2 + (dxy2 + 2dy4) = 0 Combine like terms: dxy2 + dxy2 = 2dxy2 2dxy2 + 2dy4 = 0 Solving 2dxy2 + 2dy4 = 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), '2dy2'. 2dy2(x + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'dy2' equal to zero and attempt to solve: Simplifying dy2 = 0 Solving dy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy2 = 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 + y2)' equal to zero and attempt to solve: Simplifying x + y2 = 0 Solving x + 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 + -1x + y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + y2 = 0 + -1x y2 = 0 + -1x Remove the zero: y2 = -1x Add '-1y2' to each side of the equation. y2 + -1y2 = -1x + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x + -1y2 Simplifying 0 = -1x + -1y2 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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