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

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


Simplifying
2x(y + 1) * dx + (x2 + -1) * dy = 0

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

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

Multiply x * dx
2dx2(1 + y) + (x2 + -1) * dy = 0
(1 * 2dx2 + y * 2dx2) + (x2 + -1) * dy = 0
(2dx2 + 2dx2y) + (x2 + -1) * dy = 0

Reorder the terms:
2dx2 + 2dx2y + (-1 + x2) * dy = 0

Reorder the terms for easier multiplication:
2dx2 + 2dx2y + dy(-1 + x2) = 0
2dx2 + 2dx2y + (-1 * dy + x2 * dy) = 0

Reorder the terms:
2dx2 + 2dx2y + (dx2y + -1dy) = 0
2dx2 + 2dx2y + (dx2y + -1dy) = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
2dx2 + 3dx2y + -1dy = 0

Solving
2dx2 + 3dx2y + -1dy = 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(2x2 + 3x2y + -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 '(2x2 + 3x2y + -1y)' equal to zero and attempt to solve:

Simplifying
2x2 + 3x2y + -1y = 0

Solving
2x2 + 3x2y + -1y = 0

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

Add '-2x2' to each side of the equation.
2x2 + 3x2y + -2x2 + -1y = 0 + -2x2

Reorder the terms:
2x2 + -2x2 + 3x2y + -1y = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 3x2y + -1y = 0 + -2x2
3x2y + -1y = 0 + -2x2
Remove the zero:
3x2y + -1y = -2x2

Add '-3x2y' to each side of the equation.
3x2y + -3x2y + -1y = -2x2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + -1y = -2x2 + -3x2y
-1y = -2x2 + -3x2y

Add 'y' to each side of the equation.
-1y + y = -2x2 + -3x2y + y

Combine like terms: -1y + y = 0
0 = -2x2 + -3x2y + y

Simplifying
0 = -2x2 + -3x2y + 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}

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