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

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


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

Multiply x * y
(x2 + -1xy + y2) * dx + -1(x * y) * dy = 0

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

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

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

Multiply x * y
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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