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

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

Simplifying
2y(dx) = (x2 + -1)(dx + -1dy)

Multiply y * dx
2dxy = (x2 + -1)(dx + -1dy)

Reorder the terms:
2dxy = (-1 + x2)(dx + -1dy)

Multiply (-1 + x2) * (dx + -1dy)
2dxy = (-1(dx + -1dy) + x2(dx + -1dy))
2dxy = ((dx * -1 + -1dy * -1) + x2(dx + -1dy))
2dxy = ((-1dx + 1dy) + x2(dx + -1dy))
2dxy = (-1dx + 1dy + (dx * x2 + -1dy * x2))

Reorder the terms:
2dxy = (-1dx + 1dy + (-1dx2y + dx3))
2dxy = (-1dx + 1dy + (-1dx2y + dx3))

Reorder the terms:
2dxy = (-1dx + -1dx2y + dx3 + 1dy)
2dxy = (-1dx + -1dx2y + dx3 + 1dy)

Solving
2dxy = -1dx + -1dx2y + dx3 + 1dy

Solving for variable 'd'.

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

Add 'dx' to each side of the equation.
dx + 2dxy = -1dx + -1dx2y + dx3 + dx + 1dy

Reorder the terms:
dx + 2dxy = -1dx + dx + -1dx2y + dx3 + 1dy

Combine like terms: -1dx + dx = 0
dx + 2dxy = 0 + -1dx2y + dx3 + 1dy
dx + 2dxy = -1dx2y + dx3 + 1dy

Add 'dx2y' to each side of the equation.
dx + 2dxy + dx2y = -1dx2y + dx3 + dx2y + 1dy

Reorder the terms:
dx + 2dxy + dx2y = -1dx2y + dx2y + dx3 + 1dy

Combine like terms: -1dx2y + dx2y = 0
dx + 2dxy + dx2y = 0 + dx3 + 1dy
dx + 2dxy + dx2y = dx3 + 1dy

Add '-1dx3' to each side of the equation.
dx + 2dxy + dx2y + -1dx3 = dx3 + -1dx3 + 1dy

Combine like terms: dx3 + -1dx3 = 0
dx + 2dxy + dx2y + -1dx3 = 0 + 1dy
dx + 2dxy + dx2y + -1dx3 = 1dy

Add '-1dy' to each side of the equation.
dx + 2dxy + dx2y + -1dx3 + -1dy = 1dy + -1dy

Combine like terms: 1dy + -1dy = 0
dx + 2dxy + dx2y + -1dx3 + -1dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + 2xy + x2y + -1x3 + -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 + 2xy + x2y + -1x3 + -1y)' equal to zero and attempt to solve:

Simplifying
x + 2xy + x2y + -1x3 + -1y = 0

Solving
x + 2xy + x2y + -1x3 + -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 + 2xy + x2y + -1x3 + -1x + -1y = 0 + -1x

Reorder the terms:
x + -1x + 2xy + x2y + -1x3 + -1y = 0 + -1x

Combine like terms: x + -1x = 0
0 + 2xy + x2y + -1x3 + -1y = 0 + -1x
2xy + x2y + -1x3 + -1y = 0 + -1x
Remove the zero:
2xy + x2y + -1x3 + -1y = -1x

Add '-2xy' to each side of the equation.
2xy + x2y + -1x3 + -2xy + -1y = -1x + -2xy

Reorder the terms:
2xy + -2xy + x2y + -1x3 + -1y = -1x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x2y + -1x3 + -1y = -1x + -2xy
x2y + -1x3 + -1y = -1x + -2xy

Add '-1x2y' to each side of the equation.
x2y + -1x3 + -1x2y + -1y = -1x + -2xy + -1x2y

Reorder the terms:
x2y + -1x2y + -1x3 + -1y = -1x + -2xy + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + -1x3 + -1y = -1x + -2xy + -1x2y
-1x3 + -1y = -1x + -2xy + -1x2y

Add 'x3' to each side of the equation.
-1x3 + x3 + -1y = -1x + -2xy + -1x2y + x3

Combine like terms: -1x3 + x3 = 0
0 + -1y = -1x + -2xy + -1x2y + x3
-1y = -1x + -2xy + -1x2y + x3

Add 'y' to each side of the equation.
-1y + y = -1x + -2xy + -1x2y + x3 + y

Combine like terms: -1y + y = 0
0 = -1x + -2xy + -1x2y + x3 + y

Simplifying
0 = -1x + -2xy + -1x2y + x3 + 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}