(2xy+6)dx+(x^2-3y^2)dy=0

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Solution for (2xy+6)dx+(x^2-3y^2)dy=0 equation: 


Simplifying
(2xy + 6) * dx + (x2 + -3y2) * dy = 0

Reorder the terms:
(6 + 2xy) * dx + (x2 + -3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(6 + 2xy) + (x2 + -3y2) * dy = 0
(6 * dx + 2xy * dx) + (x2 + -3y2) * dy = 0
(6dx + 2dx2y) + (x2 + -3y2) * dy = 0

Reorder the terms for easier multiplication:
6dx + 2dx2y + dy(x2 + -3y2) = 0
6dx + 2dx2y + (x2 * dy + -3y2 * dy) = 0
6dx + 2dx2y + (dx2y + -3dy3) = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
6dx + 3dx2y + -3dy3 = 0

Solving
6dx + 3dx2y + -3dy3 = 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), '3d'.
3d(2x + x2y + -1y3) = 0

Ignore the factor 3.

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 + x2y + -1y3)' equal to zero and attempt to solve:

Simplifying
2x + x2y + -1y3 = 0

Solving
2x + x2y + -1y3 = 0

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

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

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

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

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

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

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

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

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

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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