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

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

Simplifying
(y2 + 1) * dx = (1 + xy) * dy

Reorder the terms:
(1 + y2) * dx = (1 + xy) * dy

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

Reorder the terms for easier multiplication:
1dx + dxy2 = dy(1 + xy)
1dx + dxy2 = (1 * dy + xy * dy)

Reorder the terms:
1dx + dxy2 = (dxy2 + 1dy)
1dx + dxy2 = (dxy2 + 1dy)

Add '-1dxy2' to each side of the equation.
1dx + dxy2 + -1dxy2 = dxy2 + -1dxy2 + 1dy

Combine like terms: dxy2 + -1dxy2 = 0
1dx + 0 = dxy2 + -1dxy2 + 1dy
1dx = dxy2 + -1dxy2 + 1dy

Combine like terms: dxy2 + -1dxy2 = 0
1dx = 0 + 1dy
1dx = 1dy

Solving
1dx = 1dy

Solving for variable 'd'.

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

Add '-1dy' to each side of the equation.
1dx + -1dy = 1dy + -1dy

Combine like terms: 1dy + -1dy = 0
1dx + -1dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + -1y) = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add '-1x' to each side of the equation.
x + -1x + -1y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -1y = 0 + -1x
-1y = 0 + -1x
Remove the zero:
-1y = -1x

Add 'y' to each side of the equation.
-1y + y = -1x + y

Combine like terms: -1y + y = 0
0 = -1x + y

Simplifying
0 = -1x + y

The solution to this equation could not be determined.

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