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

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


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

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

Reorder the terms:
(dx2y + 1dy) = (1 + y2) * dx
(dx2y + 1dy) = (1 + y2) * dx

Reorder the terms for easier multiplication:
dx2y + 1dy = dx(1 + y2)
dx2y + 1dy = (1 * dx + y2 * dx)
dx2y + 1dy = (1dx + dxy2)

Solving
dx2y + 1dy = 1dx + dxy2

Solving for variable 'd'.

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

Add '-1dx' to each side of the equation.
dx2y + -1dx + 1dy = 1dx + -1dx + dxy2

Reorder the terms:
-1dx + dx2y + 1dy = 1dx + -1dx + dxy2

Combine like terms: 1dx + -1dx = 0
-1dx + dx2y + 1dy = 0 + dxy2
-1dx + dx2y + 1dy = dxy2

Add '-1dxy2' to each side of the equation.
-1dx + dx2y + -1dxy2 + 1dy = dxy2 + -1dxy2

Reorder the terms:
-1dx + -1dxy2 + dx2y + 1dy = dxy2 + -1dxy2

Combine like terms: dxy2 + -1dxy2 = 0
-1dx + -1dxy2 + dx2y + 1dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1x + -1xy2 + x2y + y) = 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 '(-1x + -1xy2 + x2y + y)' equal to zero and attempt to solve:

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

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

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

Add 'x' to each side of the equation.
-1x + -1xy2 + x2y + x + y = 0 + x

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

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

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

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

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

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

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

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

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

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

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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