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

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


Simplifying
(x2 + y2 + -1) * dy + 2(xy + 1) * dx = 0

Reorder the terms:
(-1 + x2 + y2) * dy + 2(xy + 1) * dx = 0

Reorder the terms for easier multiplication:
dy(-1 + x2 + y2) + 2(xy + 1) * dx = 0
(-1 * dy + x2 * dy + y2 * dy) + 2(xy + 1) * dx = 0

Reorder the terms:
(dx2y + -1dy + dy3) + 2(xy + 1) * dx = 0
(dx2y + -1dy + dy3) + 2(xy + 1) * dx = 0

Reorder the terms:
dx2y + -1dy + dy3 + 2(1 + xy) * dx = 0

Reorder the terms for easier multiplication:
dx2y + -1dy + dy3 + 2dx(1 + xy) = 0
dx2y + -1dy + dy3 + (1 * 2dx + xy * 2dx) = 0
dx2y + -1dy + dy3 + (2dx + 2dx2y) = 0

Reorder the terms:
2dx + dx2y + 2dx2y + -1dy + dy3 = 0

Combine like terms: dx2y + 2dx2y = 3dx2y
2dx + 3dx2y + -1dy + dy3 = 0

Solving
2dx + 3dx2y + -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(2x + 3x2y + -1y + 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 '(2x + 3x2y + -1y + y3)' equal to zero and attempt to solve:

Simplifying
2x + 3x2y + -1y + y3 = 0

Solving
2x + 3x2y + -1y + y3 = 0

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

Add '-2x' to each side of the equation.
2x + 3x2y + -1y + -2x + y3 = 0 + -2x

Reorder the terms:
2x + -2x + 3x2y + -1y + y3 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 3x2y + -1y + y3 = 0 + -2x
3x2y + -1y + y3 = 0 + -2x
Remove the zero:
3x2y + -1y + y3 = -2x

Add '-3x2y' to each side of the equation.
3x2y + -1y + -3x2y + y3 = -2x + -3x2y

Reorder the terms:
3x2y + -3x2y + -1y + y3 = -2x + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + -1y + y3 = -2x + -3x2y
-1y + y3 = -2x + -3x2y

Add 'y' to each side of the equation.
-1y + y + y3 = -2x + -3x2y + y

Combine like terms: -1y + y = 0
0 + y3 = -2x + -3x2y + y
y3 = -2x + -3x2y + y

Add '-1y3' to each side of the equation.
y3 + -1y3 = -2x + -3x2y + y + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -2x + -3x2y + y + -1y3

Simplifying
0 = -2x + -3x2y + y + -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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