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

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


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

Reorder the terms:
(1 + y2) * dx + y(x2 + -1) * dy = 0

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

Reorder the terms:
1dx + dxy2 + y(-1 + x2) * dy = 0

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

Multiply y * dy
1dx + dxy2 + dy2(-1 + x2) = 0
1dx + dxy2 + (-1 * dy2 + x2 * dy2) = 0

Reorder the terms:
1dx + dxy2 + (dx2y2 + -1dy2) = 0
1dx + dxy2 + (dx2y2 + -1dy2) = 0

Solving
1dx + dxy2 + dx2y2 + -1dy2 = 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 + x2y2 + -1y2) = 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 + x2y2 + -1y2)' equal to zero and attempt to solve:

Simplifying
x + xy2 + x2y2 + -1y2 = 0

Solving
x + xy2 + x2y2 + -1y2 = 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 + x2y2 + -1x + -1y2 = 0 + -1x

Reorder the terms:
x + -1x + xy2 + x2y2 + -1y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy2 + x2y2 + -1y2 = 0 + -1x
xy2 + x2y2 + -1y2 = 0 + -1x
Remove the zero:
xy2 + x2y2 + -1y2 = -1x

Add '-1xy2' to each side of the equation.
xy2 + x2y2 + -1xy2 + -1y2 = -1x + -1xy2

Reorder the terms:
xy2 + -1xy2 + x2y2 + -1y2 = -1x + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x2y2 + -1y2 = -1x + -1xy2
x2y2 + -1y2 = -1x + -1xy2

Add '-1x2y2' to each side of the equation.
x2y2 + -1x2y2 + -1y2 = -1x + -1xy2 + -1x2y2

Combine like terms: x2y2 + -1x2y2 = 0
0 + -1y2 = -1x + -1xy2 + -1x2y2
-1y2 = -1x + -1xy2 + -1x2y2

Add 'y2' to each side of the equation.
-1y2 + y2 = -1x + -1xy2 + -1x2y2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -1x + -1xy2 + -1x2y2 + y2

Simplifying
0 = -1x + -1xy2 + -1x2y2 + y2

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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