(4xy+6x^3)dx+(2x^2+3y)dy=0

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Solution for (4xy+6x^3)dx+(2x^2+3y)dy=0 equation: 


Simplifying
(4xy + 6x3) * dx + (2x2 + 3y) * dy = 0

Reorder the terms for easier multiplication:
dx(4xy + 6x3) + (2x2 + 3y) * dy = 0
(4xy * dx + 6x3 * dx) + (2x2 + 3y) * dy = 0
(4dx2y + 6dx4) + (2x2 + 3y) * dy = 0

Reorder the terms for easier multiplication:
4dx2y + 6dx4 + dy(2x2 + 3y) = 0
4dx2y + 6dx4 + (2x2 * dy + 3y * dy) = 0
4dx2y + 6dx4 + (2dx2y + 3dy2) = 0

Reorder the terms:
4dx2y + 2dx2y + 6dx4 + 3dy2 = 0

Combine like terms: 4dx2y + 2dx2y = 6dx2y
6dx2y + 6dx4 + 3dy2 = 0

Solving
6dx2y + 6dx4 + 3dy2 = 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(2x2y + 2x4 + y2) = 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 '(2x2y + 2x4 + y2)' equal to zero and attempt to solve:

Simplifying
2x2y + 2x4 + y2 = 0

Solving
2x2y + 2x4 + y2 = 0

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

Add '-2x2y' to each side of the equation.
2x2y + 2x4 + -2x2y + y2 = 0 + -2x2y

Reorder the terms:
2x2y + -2x2y + 2x4 + y2 = 0 + -2x2y

Combine like terms: 2x2y + -2x2y = 0
0 + 2x4 + y2 = 0 + -2x2y
2x4 + y2 = 0 + -2x2y
Remove the zero:
2x4 + y2 = -2x2y

Add '-2x4' to each side of the equation.
2x4 + -2x4 + y2 = -2x2y + -2x4

Combine like terms: 2x4 + -2x4 = 0
0 + y2 = -2x2y + -2x4
y2 = -2x2y + -2x4

Add '-1y2' to each side of the equation.
y2 + -1y2 = -2x2y + -2x4 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -2x2y + -2x4 + -1y2

Simplifying
0 = -2x2y + -2x4 + -1y2

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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