(y^3-2x^2y)dx+(2xy^2-x^3)dy=0

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Solution for (y^3-2x^2y)dx+(2xy^2-x^3)dy=0 equation:


Simplifying
(y3 + -2x2y) * dx + (2xy2 + -1x3) * dy = 0

Reorder the terms:
(-2x2y + y3) * dx + (2xy2 + -1x3) * dy = 0

Reorder the terms for easier multiplication:
dx(-2x2y + y3) + (2xy2 + -1x3) * dy = 0
(-2x2y * dx + y3 * dx) + (2xy2 + -1x3) * dy = 0

Reorder the terms:
(dxy3 + -2dx3y) + (2xy2 + -1x3) * dy = 0
(dxy3 + -2dx3y) + (2xy2 + -1x3) * dy = 0

Reorder the terms for easier multiplication:
dxy3 + -2dx3y + dy(2xy2 + -1x3) = 0
dxy3 + -2dx3y + (2xy2 * dy + -1x3 * dy) = 0
dxy3 + -2dx3y + (2dxy3 + -1dx3y) = 0

Reorder the terms:
dxy3 + 2dxy3 + -2dx3y + -1dx3y = 0

Combine like terms: dxy3 + 2dxy3 = 3dxy3
3dxy3 + -2dx3y + -1dx3y = 0

Combine like terms: -2dx3y + -1dx3y = -3dx3y
3dxy3 + -3dx3y = 0

Solving
3dxy3 + -3dx3y = 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), '3dxy'.
3dxy(y2 + -1x2) = 0

Factor a difference between two squares.
3dxy((y + x)(y + -1x)) = 0

Ignore the factor 3.

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 '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 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 + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

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