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

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


Simplifying
(4xy + y2) * dx + (4x + 2y + -4) * dy = 0

Reorder the terms for easier multiplication:
dx(4xy + y2) + (4x + 2y + -4) * dy = 0
(4xy * dx + y2 * dx) + (4x + 2y + -4) * dy = 0

Reorder the terms:
(dxy2 + 4dx2y) + (4x + 2y + -4) * dy = 0
(dxy2 + 4dx2y) + (4x + 2y + -4) * dy = 0

Reorder the terms:
dxy2 + 4dx2y + (-4 + 4x + 2y) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 4dx2y + dy(-4 + 4x + 2y) = 0
dxy2 + 4dx2y + (-4 * dy + 4x * dy + 2y * dy) = 0

Reorder the terms:
dxy2 + 4dx2y + (4dxy + -4dy + 2dy2) = 0
dxy2 + 4dx2y + (4dxy + -4dy + 2dy2) = 0

Reorder the terms:
4dxy + dxy2 + 4dx2y + -4dy + 2dy2 = 0

Solving
4dxy + dxy2 + 4dx2y + -4dy + 2dy2 = 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), 'dy'.
dy(4x + xy + 4x2 + -4 + 2y) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(4x + xy + 4x2 + -4 + 2y)' equal to zero and attempt to solve:

Simplifying
4x + xy + 4x2 + -4 + 2y = 0

Reorder the terms:
-4 + 4x + xy + 4x2 + 2y = 0

Solving
-4 + 4x + xy + 4x2 + 2y = 0

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

Add '4' to each side of the equation.
-4 + 4x + xy + 4x2 + 4 + 2y = 0 + 4

Reorder the terms:
-4 + 4 + 4x + xy + 4x2 + 2y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4x + xy + 4x2 + 2y = 0 + 4
4x + xy + 4x2 + 2y = 0 + 4

Combine like terms: 0 + 4 = 4
4x + xy + 4x2 + 2y = 4

Add '-4x' to each side of the equation.
4x + xy + 4x2 + -4x + 2y = 4 + -4x

Reorder the terms:
4x + -4x + xy + 4x2 + 2y = 4 + -4x

Combine like terms: 4x + -4x = 0
0 + xy + 4x2 + 2y = 4 + -4x
xy + 4x2 + 2y = 4 + -4x

Add '-1xy' to each side of the equation.
xy + 4x2 + -1xy + 2y = 4 + -4x + -1xy

Reorder the terms:
xy + -1xy + 4x2 + 2y = 4 + -4x + -1xy

Combine like terms: xy + -1xy = 0
0 + 4x2 + 2y = 4 + -4x + -1xy
4x2 + 2y = 4 + -4x + -1xy

Add '-4x2' to each side of the equation.
4x2 + -4x2 + 2y = 4 + -4x + -1xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 2y = 4 + -4x + -1xy + -4x2
2y = 4 + -4x + -1xy + -4x2

Add '-2y' to each side of the equation.
2y + -2y = 4 + -4x + -1xy + -4x2 + -2y

Combine like terms: 2y + -2y = 0
0 = 4 + -4x + -1xy + -4x2 + -2y

Simplifying
0 = 4 + -4x + -1xy + -4x2 + -2y

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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