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

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


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

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

Reorder the terms for easier multiplication:
1dx + dxy2 + dy(1 + y2) = 0
1dx + dxy2 + (1 * dy + y2 * dy) = 0
1dx + dxy2 + (1dy + dy3) = 0

Solving
1dx + dxy2 + 1dy + dy3 = 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 + y + y3) = 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 + y + y3)' equal to zero and attempt to solve:

Simplifying
x + xy2 + y + y3 = 0

Solving
x + xy2 + y + y3 = 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 + y + -1x + y3 = 0 + -1x

Reorder the terms:
x + -1x + xy2 + y + y3 = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy2 + y + y3 = 0 + -1x
xy2 + y + y3 = 0 + -1x
Remove the zero:
xy2 + y + y3 = -1x

Add '-1xy2' to each side of the equation.
xy2 + y + -1xy2 + y3 = -1x + -1xy2

Reorder the terms:
xy2 + -1xy2 + y + y3 = -1x + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + y + y3 = -1x + -1xy2
y + y3 = -1x + -1xy2

Add '-1y' to each side of the equation.
y + -1y + y3 = -1x + -1xy2 + -1y

Combine like terms: y + -1y = 0
0 + y3 = -1x + -1xy2 + -1y
y3 = -1x + -1xy2 + -1y

Add '-1y3' to each side of the equation.
y3 + -1y3 = -1x + -1xy2 + -1y + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -1x + -1xy2 + -1y + -1y3

Simplifying
0 = -1x + -1xy2 + -1y + -1y3

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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