(1+4xy+2y^2)dx+(1+4xy+2x^2)dy=0

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Solution for (1+4xy+2y^2)dx+(1+4xy+2x^2)dy=0 equation: 


Simplifying
(1 + 4xy + 2y2) * dx + (1 + 4xy + 2x2) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 4xy + 2y2) + (1 + 4xy + 2x2) * dy = 0
(1 * dx + 4xy * dx + 2y2 * dx) + (1 + 4xy + 2x2) * dy = 0

Reorder the terms:
(1dx + 2dxy2 + 4dx2y) + (1 + 4xy + 2x2) * dy = 0
(1dx + 2dxy2 + 4dx2y) + (1 + 4xy + 2x2) * dy = 0

Reorder the terms for easier multiplication:
1dx + 2dxy2 + 4dx2y + dy(1 + 4xy + 2x2) = 0
1dx + 2dxy2 + 4dx2y + (1 * dy + 4xy * dy + 2x2 * dy) = 0

Reorder the terms:
1dx + 2dxy2 + 4dx2y + (4dxy2 + 2dx2y + 1dy) = 0
1dx + 2dxy2 + 4dx2y + (4dxy2 + 2dx2y + 1dy) = 0

Reorder the terms:
1dx + 2dxy2 + 4dxy2 + 4dx2y + 2dx2y + 1dy = 0

Combine like terms: 2dxy2 + 4dxy2 = 6dxy2
1dx + 6dxy2 + 4dx2y + 2dx2y + 1dy = 0

Combine like terms: 4dx2y + 2dx2y = 6dx2y
1dx + 6dxy2 + 6dx2y + 1dy = 0

Solving
1dx + 6dxy2 + 6dx2y + 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 + 6xy2 + 6x2y + 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 + 6xy2 + 6x2y + y)' equal to zero and attempt to solve:

Simplifying
x + 6xy2 + 6x2y + y = 0

Solving
x + 6xy2 + 6x2y + 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 + 6xy2 + 6x2y + -1x + y = 0 + -1x

Reorder the terms:
x + -1x + 6xy2 + 6x2y + y = 0 + -1x

Combine like terms: x + -1x = 0
0 + 6xy2 + 6x2y + y = 0 + -1x
6xy2 + 6x2y + y = 0 + -1x
Remove the zero:
6xy2 + 6x2y + y = -1x

Add '-6xy2' to each side of the equation.
6xy2 + 6x2y + -6xy2 + y = -1x + -6xy2

Reorder the terms:
6xy2 + -6xy2 + 6x2y + y = -1x + -6xy2

Combine like terms: 6xy2 + -6xy2 = 0
0 + 6x2y + y = -1x + -6xy2
6x2y + y = -1x + -6xy2

Add '-6x2y' to each side of the equation.
6x2y + -6x2y + y = -1x + -6xy2 + -6x2y

Combine like terms: 6x2y + -6x2y = 0
0 + y = -1x + -6xy2 + -6x2y
y = -1x + -6xy2 + -6x2y

Add '-1y' to each side of the equation.
y + -1y = -1x + -6xy2 + -6x2y + -1y

Combine like terms: y + -1y = 0
0 = -1x + -6xy2 + -6x2y + -1y

Simplifying
0 = -1x + -6xy2 + -6x2y + -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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