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

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

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

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

Reorder the terms:
(1dx + dxy2 + dx2) + 2y * dy = 0
(1dx + dxy2 + dx2) + 2y * dy = 0

Multiply y * dy
1dx + dxy2 + dx2 + 2dy2 = 0

Solving
1dx + dxy2 + dx2 + 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), 'd'.
d(x + xy2 + x2 + 2y2) = 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 + x2 + 2y2)' equal to zero and attempt to solve:

Simplifying
x + xy2 + x2 + 2y2 = 0

Solving
x + xy2 + x2 + 2y2 = 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 + x2 + -1x + 2y2 = 0 + -1x

Reorder the terms:
x + -1x + xy2 + x2 + 2y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy2 + x2 + 2y2 = 0 + -1x
xy2 + x2 + 2y2 = 0 + -1x
Remove the zero:
xy2 + x2 + 2y2 = -1x

Add '-1xy2' to each side of the equation.
xy2 + x2 + -1xy2 + 2y2 = -1x + -1xy2

Reorder the terms:
xy2 + -1xy2 + x2 + 2y2 = -1x + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x2 + 2y2 = -1x + -1xy2
x2 + 2y2 = -1x + -1xy2

Add '-1x2' to each side of the equation.
x2 + -1x2 + 2y2 = -1x + -1xy2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 2y2 = -1x + -1xy2 + -1x2
2y2 = -1x + -1xy2 + -1x2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x + -1xy2 + -1x2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x + -1xy2 + -1x2 + -2y2

Simplifying
0 = -1x + -1xy2 + -1x2 + -2y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}