(2xy+3)dx+(x^2-1)dy=0

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Solution for (2xy+3)dx+(x^2-1)dy=0 equation: 


Simplifying
(2xy + 3) * dx + (x2 + -1) * dy = 0

Reorder the terms:
(3 + 2xy) * dx + (x2 + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 2xy) + (x2 + -1) * dy = 0
(3 * dx + 2xy * dx) + (x2 + -1) * dy = 0
(3dx + 2dx2y) + (x2 + -1) * dy = 0

Reorder the terms:
3dx + 2dx2y + (-1 + x2) * dy = 0

Reorder the terms for easier multiplication:
3dx + 2dx2y + dy(-1 + x2) = 0
3dx + 2dx2y + (-1 * dy + x2 * dy) = 0

Reorder the terms:
3dx + 2dx2y + (dx2y + -1dy) = 0
3dx + 2dx2y + (dx2y + -1dy) = 0

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -3x + -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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