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

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


Simplifying
(1 + y2) * dx + (x2y + y + 2xy) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + y2) + (x2y + y + 2xy) * dy = 0
(1 * dx + y2 * dx) + (x2y + y + 2xy) * dy = 0
(1dx + dxy2) + (x2y + y + 2xy) * dy = 0

Reorder the terms:
1dx + dxy2 + (2xy + x2y + y) * dy = 0

Reorder the terms for easier multiplication:
1dx + dxy2 + dy(2xy + x2y + y) = 0
1dx + dxy2 + (2xy * dy + x2y * dy + y * dy) = 0
1dx + dxy2 + (2dxy2 + dx2y2 + dy2) = 0

Combine like terms: dxy2 + 2dxy2 = 3dxy2
1dx + 3dxy2 + dx2y2 + dy2 = 0

Solving
1dx + 3dxy2 + dx2y2 + 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(x + 3xy2 + x2y2 + 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 '(x + 3xy2 + x2y2 + y2)' equal to zero and attempt to solve:

Simplifying
x + 3xy2 + x2y2 + y2 = 0

Solving
x + 3xy2 + x2y2 + y2 = 0

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

Add '-1x' to each side of the equation.
x + 3xy2 + x2y2 + -1x + y2 = 0 + -1x

Reorder the terms:
x + -1x + 3xy2 + x2y2 + y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 3xy2 + x2y2 + y2 = 0 + -1x
3xy2 + x2y2 + y2 = 0 + -1x
Remove the zero:
3xy2 + x2y2 + y2 = -1x

Add '-3xy2' to each side of the equation.
3xy2 + x2y2 + -3xy2 + y2 = -1x + -3xy2

Reorder the terms:
3xy2 + -3xy2 + x2y2 + y2 = -1x + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + x2y2 + y2 = -1x + -3xy2
x2y2 + y2 = -1x + -3xy2

Add '-1x2y2' to each side of the equation.
x2y2 + -1x2y2 + y2 = -1x + -3xy2 + -1x2y2

Combine like terms: x2y2 + -1x2y2 = 0
0 + y2 = -1x + -3xy2 + -1x2y2
y2 = -1x + -3xy2 + -1x2y2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1x + -3xy2 + -1x2y2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1x + -3xy2 + -1x2y2 + -1y2

Simplifying
0 = -1x + -3xy2 + -1x2y2 + -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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