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

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


Simplifying
(4x + xy2) * dx + (y + x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(4x + xy2) + (y + x2y) * dy = 0
(4x * dx + xy2 * dx) + (y + x2y) * dy = 0
(4dx2 + dx2y2) + (y + x2y) * dy = 0

Reorder the terms:
4dx2 + dx2y2 + (x2y + y) * dy = 0

Reorder the terms for easier multiplication:
4dx2 + dx2y2 + dy(x2y + y) = 0
4dx2 + dx2y2 + (x2y * dy + y * dy) = 0
4dx2 + dx2y2 + (dx2y2 + dy2) = 0

Combine like terms: dx2y2 + dx2y2 = 2dx2y2
4dx2 + 2dx2y2 + dy2 = 0

Solving
4dx2 + 2dx2y2 + dy2 = 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(4x2 + 2x2y2 + y2) = 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 '(4x2 + 2x2y2 + y2)' equal to zero and attempt to solve:

Simplifying
4x2 + 2x2y2 + y2 = 0

Solving
4x2 + 2x2y2 + y2 = 0

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

Add '-4x2' to each side of the equation.
4x2 + 2x2y2 + -4x2 + y2 = 0 + -4x2

Reorder the terms:
4x2 + -4x2 + 2x2y2 + y2 = 0 + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 2x2y2 + y2 = 0 + -4x2
2x2y2 + y2 = 0 + -4x2
Remove the zero:
2x2y2 + y2 = -4x2

Add '-2x2y2' to each side of the equation.
2x2y2 + -2x2y2 + y2 = -4x2 + -2x2y2

Combine like terms: 2x2y2 + -2x2y2 = 0
0 + y2 = -4x2 + -2x2y2
y2 = -4x2 + -2x2y2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -4x2 + -2x2y2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -4x2 + -2x2y2 + -1y2

Simplifying
0 = -4x2 + -2x2y2 + -1y2

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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