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Simplifying xdy + -1ydx = 4y(x2 + y2) * dx Combine like terms: dxy + -1dxy = 0 0 = 4y(x2 + y2) * dx Reorder the terms for easier multiplication: 0 = 4y * dx(x2 + y2) Multiply y * dx 0 = 4dxy(x2 + y2) 0 = (x2 * 4dxy + y2 * 4dxy) Reorder the terms: 0 = (4dxy3 + 4dx3y) 0 = (4dxy3 + 4dx3y) Solving 0 = 4dxy3 + 4dx3y Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4dxy3' to each side of the equation. 0 + -4dxy3 = 4dxy3 + -4dxy3 + 4dx3y Remove the zero: -4dxy3 = 4dxy3 + -4dxy3 + 4dx3y Combine like terms: 4dxy3 + -4dxy3 = 0 -4dxy3 = 0 + 4dx3y -4dxy3 = 4dx3y Add '-4dx3y' to each side of the equation. -4dxy3 + -4dx3y = 4dx3y + -4dx3y Combine like terms: 4dx3y + -4dx3y = 0 -4dxy3 + -4dx3y = 0 Factor out the Greatest Common Factor (GCF), '-4dxy'. -4dxy(y2 + x2) = 0 Ignore the factor -4.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 '(y2 + x2)' equal to zero and attempt to solve: Simplifying y2 + x2 = 0 Reorder the terms: x2 + y2 = 0 Solving x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 0 + -1x2 y2 = 0 + -1x2 Remove the zero: y2 = -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x2 + -1y2 Simplifying 0 = -1x2 + -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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