dy+(xy-xy^3)dx=0

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Solution for dy+(xy-xy^3)dx=0 equation:


Simplifying
dy + (xy + -1xy3) * dx = 0

Reorder the terms for easier multiplication:
dy + dx(xy + -1xy3) = 0
dy + (xy * dx + -1xy3 * dx) = 0
dy + (dx2y + -1dx2y3) = 0

Reorder the terms:
dx2y + -1dx2y3 + dy = 0

Solving
dx2y + -1dx2y3 + dy = 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), 'dy'.
dy(x2 + -1x2y2 + 1) = 0

Subproblem 1

Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(x2 + -1x2y2 + 1)' equal to zero and attempt to solve: Simplifying x2 + -1x2y2 + 1 = 0 Reorder the terms: 1 + x2 + -1x2y2 = 0 Solving 1 + x2 + -1x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + x2 + -1 + -1x2y2 = 0 + -1 Reorder the terms: 1 + -1 + x2 + -1x2y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 + -1x2y2 = 0 + -1 x2 + -1x2y2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 + -1x2y2 = -1 Add '-1x2' to each side of the equation. x2 + -1x2 + -1x2y2 = -1 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1x2y2 = -1 + -1x2 -1x2y2 = -1 + -1x2 Add 'x2y2' to each side of the equation. -1x2y2 + x2y2 = -1 + -1x2 + x2y2 Combine like terms: -1x2y2 + x2y2 = 0 0 = -1 + -1x2 + x2y2 Simplifying 0 = -1 + -1x2 + x2y2 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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