(y^2+xy+1)dx+(x^2+xy+1)dy=0

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Solution for (y^2+xy+1)dx+(x^2+xy+1)dy=0 equation: 


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

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

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

Reorder the terms:
(1dx + dxy2 + dx2y) + (x2 + xy + 1) * dy = 0
(1dx + dxy2 + dx2y) + (x2 + xy + 1) * dy = 0

Reorder the terms:
1dx + dxy2 + dx2y + (1 + xy + x2) * dy = 0

Reorder the terms for easier multiplication:
1dx + dxy2 + dx2y + dy(1 + xy + x2) = 0
1dx + dxy2 + dx2y + (1 * dy + xy * dy + x2 * dy) = 0

Reorder the terms:
1dx + dxy2 + dx2y + (dxy2 + dx2y + 1dy) = 0
1dx + dxy2 + dx2y + (dxy2 + dx2y + 1dy) = 0

Reorder the terms:
1dx + dxy2 + dxy2 + dx2y + dx2y + 1dy = 0

Combine like terms: dxy2 + dxy2 = 2dxy2
1dx + 2dxy2 + dx2y + dx2y + 1dy = 0

Combine like terms: dx2y + dx2y = 2dx2y
1dx + 2dxy2 + 2dx2y + 1dy = 0

Solving
1dx + 2dxy2 + 2dx2y + 1dy = 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(x + 2xy2 + 2x2y + y) = 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 '(x + 2xy2 + 2x2y + y)' equal to zero and attempt to solve:

Simplifying
x + 2xy2 + 2x2y + y = 0

Solving
x + 2xy2 + 2x2y + 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 + 2xy2 + 2x2y + -1x + y = 0 + -1x

Reorder the terms:
x + -1x + 2xy2 + 2x2y + y = 0 + -1x

Combine like terms: x + -1x = 0
0 + 2xy2 + 2x2y + y = 0 + -1x
2xy2 + 2x2y + y = 0 + -1x
Remove the zero:
2xy2 + 2x2y + y = -1x

Add '-2xy2' to each side of the equation.
2xy2 + 2x2y + -2xy2 + y = -1x + -2xy2

Reorder the terms:
2xy2 + -2xy2 + 2x2y + y = -1x + -2xy2

Combine like terms: 2xy2 + -2xy2 = 0
0 + 2x2y + y = -1x + -2xy2
2x2y + y = -1x + -2xy2

Add '-2x2y' to each side of the equation.
2x2y + -2x2y + y = -1x + -2xy2 + -2x2y

Combine like terms: 2x2y + -2x2y = 0
0 + y = -1x + -2xy2 + -2x2y
y = -1x + -2xy2 + -2x2y

Add '-1y' to each side of the equation.
y + -1y = -1x + -2xy2 + -2x2y + -1y

Combine like terms: y + -1y = 0
0 = -1x + -2xy2 + -2x2y + -1y

Simplifying
0 = -1x + -2xy2 + -2x2y + -1y

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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