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

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


Simplifying
(x2 + -1xy + y2) * dx + -1(xy) * dy = 0

Reorder the terms:
(-1xy + x2 + y2) * dx + -1(xy) * dy = 0

Reorder the terms for easier multiplication:
dx(-1xy + x2 + y2) + -1(xy) * dy = 0
(-1xy * dx + x2 * dx + y2 * dx) + -1(xy) * dy = 0

Reorder the terms:
(dxy2 + -1dx2y + dx3) + -1(xy) * dy = 0
(dxy2 + -1dx2y + dx3) + -1(xy) * dy = 0

Multiply xy * dy
dxy2 + -1dx2y + dx3 + -1dxy2 = 0

Reorder the terms:
dxy2 + -1dxy2 + -1dx2y + dx3 = 0

Combine like terms: dxy2 + -1dxy2 = 0
0 + -1dx2y + dx3 = 0
-1dx2y + dx3 = 0

Solving
-1dx2y + dx3 = 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), 'dx2'.
dx2(-1y + x) = 0

Subproblem 1

Set the factor 'dx2' equal to zero and attempt to solve: Simplifying dx2 = 0 Solving dx2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2 = 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 '(-1y + x)' equal to zero and attempt to solve: Simplifying -1y + x = 0 Reorder the terms: x + -1y = 0 Solving x + -1y = 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 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y 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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