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

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

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

Reorder the terms for easier multiplication:
dx(1 + y2) + (x2 + y) * dy = 0
(1 * dx + y2 * dx) + (x2 + y) * dy = 0
(1dx + dxy2) + (x2 + y) * dy = 0

Reorder the terms for easier multiplication:
1dx + dxy2 + dy(x2 + y) = 0
1dx + dxy2 + (x2 * dy + y * dy) = 0
1dx + dxy2 + (dx2y + dy2) = 0

Solving
1dx + dxy2 + dx2y + 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 + xy2 + x2y + 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 + xy2 + x2y + y2)' equal to zero and attempt to solve:

Simplifying
x + xy2 + x2y + y2 = 0

Solving
x + xy2 + x2y + 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 + xy2 + x2y + -1x + y2 = 0 + -1x

Reorder the terms:
x + -1x + xy2 + x2y + y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy2 + x2y + y2 = 0 + -1x
xy2 + x2y + y2 = 0 + -1x
Remove the zero:
xy2 + x2y + y2 = -1x

Add '-1xy2' to each side of the equation.
xy2 + x2y + -1xy2 + y2 = -1x + -1xy2

Reorder the terms:
xy2 + -1xy2 + x2y + y2 = -1x + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x2y + y2 = -1x + -1xy2
x2y + y2 = -1x + -1xy2

Add '-1x2y' to each side of the equation.
x2y + -1x2y + y2 = -1x + -1xy2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + y2 = -1x + -1xy2 + -1x2y
y2 = -1x + -1xy2 + -1x2y

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1x + -1xy2 + -1x2y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1x + -1xy2 + -1x2y + -1y2

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