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

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


Simplifying
(x2 + 2xy + -1y2) * dx + -1(x2 + -2xy + -1y2) * dy = 0

Reorder the terms:
(2xy + x2 + -1y2) * dx + -1(x2 + -2xy + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + x2 + -1y2) + -1(x2 + -2xy + -1y2) * dy = 0
(2xy * dx + x2 * dx + -1y2 * dx) + -1(x2 + -2xy + -1y2) * dy = 0

Reorder the terms:
(-1dxy2 + 2dx2y + dx3) + -1(x2 + -2xy + -1y2) * dy = 0
(-1dxy2 + 2dx2y + dx3) + -1(x2 + -2xy + -1y2) * dy = 0

Reorder the terms:
-1dxy2 + 2dx2y + dx3 + -1(-2xy + x2 + -1y2) * dy = 0

Reorder the terms for easier multiplication:
-1dxy2 + 2dx2y + dx3 + -1dy(-2xy + x2 + -1y2) = 0
-1dxy2 + 2dx2y + dx3 + (-2xy * -1dy + x2 * -1dy + -1y2 * -1dy) = 0
-1dxy2 + 2dx2y + dx3 + (2dxy2 + -1dx2y + 1dy3) = 0

Reorder the terms:
-1dxy2 + 2dxy2 + 2dx2y + -1dx2y + dx3 + 1dy3 = 0

Combine like terms: -1dxy2 + 2dxy2 = 1dxy2
1dxy2 + 2dx2y + -1dx2y + dx3 + 1dy3 = 0

Combine like terms: 2dx2y + -1dx2y = 1dx2y
1dxy2 + 1dx2y + dx3 + 1dy3 = 0

Solving
1dxy2 + 1dx2y + dx3 + 1dy3 = 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), 'd'.
d(xy2 + x2y + x3 + y3) = 0


Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
d = 0

Subproblem 2
Set the factor '(xy2 + x2y + x3 + y3)' equal to zero and attempt to solve:

Simplifying
xy2 + x2y + x3 + y3 = 0

Solving
xy2 + x2y + x3 + y3 = 0

Move all terms containing d to the left, all other terms to the right.

Add '-1xy2' to each side of the equation.
xy2 + x2y + x3 + -1xy2 + y3 = 0 + -1xy2

Reorder the terms:
xy2 + -1xy2 + x2y + x3 + y3 = 0 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x2y + x3 + y3 = 0 + -1xy2
x2y + x3 + y3 = 0 + -1xy2
Remove the zero:
x2y + x3 + y3 = -1xy2

Add '-1x2y' to each side of the equation.
x2y + x3 + -1x2y + y3 = -1xy2 + -1x2y

Reorder the terms:
x2y + -1x2y + x3 + y3 = -1xy2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + x3 + y3 = -1xy2 + -1x2y
x3 + y3 = -1xy2 + -1x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + y3 = -1xy2 + -1x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + y3 = -1xy2 + -1x2y + -1x3
y3 = -1xy2 + -1x2y + -1x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = -1xy2 + -1x2y + -1x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -1xy2 + -1x2y + -1x3 + -1y3

Simplifying
0 = -1xy2 + -1x2y + -1x3 + -1y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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