Simplifying ydx + x(1 + -3x2y2) * dy = 0 Reorder the terms for easier multiplication: dxy + x * dy(1 + -3x2y2) = 0 Multiply x * dy dxy + dxy(1 + -3x2y2) = 0 dxy + (1 * dxy + -3x2y2 * dxy) = 0 dxy + (1dxy + -3dx3y3) = 0 Combine like terms: dxy + 1dxy = 2dxy 2dxy + -3dx3y3 = 0 Solving 2dxy + -3dx3y3 = 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), 'dxy'. dxy(2 + -3x2y2) = 0

Subproblem 1

Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(2 + -3x2y2)' equal to zero and attempt to solve: Simplifying 2 + -3x2y2 = 0 Solving 2 + -3x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x2y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x2y2 = 0 + -2 -3x2y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3x2y2 = -2 Add '3x2y2' to each side of the equation. -3x2y2 + 3x2y2 = -2 + 3x2y2 Combine like terms: -3x2y2 + 3x2y2 = 0 0 = -2 + 3x2y2 Simplifying 0 = -2 + 3x2y2 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.