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

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


Simplifying
(y2 + 6x2y) * dx + (2xy + 2x3) * dy = 0

Reorder the terms:
(6x2y + y2) * dx + (2xy + 2x3) * dy = 0

Reorder the terms for easier multiplication:
dx(6x2y + y2) + (2xy + 2x3) * dy = 0
(6x2y * dx + y2 * dx) + (2xy + 2x3) * dy = 0

Reorder the terms:
(dxy2 + 6dx3y) + (2xy + 2x3) * dy = 0
(dxy2 + 6dx3y) + (2xy + 2x3) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 6dx3y + dy(2xy + 2x3) = 0
dxy2 + 6dx3y + (2xy * dy + 2x3 * dy) = 0
dxy2 + 6dx3y + (2dxy2 + 2dx3y) = 0

Reorder the terms:
dxy2 + 2dxy2 + 6dx3y + 2dx3y = 0

Combine like terms: dxy2 + 2dxy2 = 3dxy2
3dxy2 + 6dx3y + 2dx3y = 0

Combine like terms: 6dx3y + 2dx3y = 8dx3y
3dxy2 + 8dx3y = 0

Solving
3dxy2 + 8dx3y = 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), 'dxy'.
dxy(3y + 8x2) = 0


Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve:

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3y + 8x2)' equal to zero and attempt to solve:

Simplifying
3y + 8x2 = 0

Reorder the terms:
8x2 + 3y = 0

Solving
8x2 + 3y = 0

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

Add '-8x2' to each side of the equation.
8x2 + -8x2 + 3y = 0 + -8x2

Combine like terms: 8x2 + -8x2 = 0
0 + 3y = 0 + -8x2
3y = 0 + -8x2
Remove the zero:
3y = -8x2

Add '-3y' to each side of the equation.
3y + -3y = -8x2 + -3y

Combine like terms: 3y + -3y = 0
0 = -8x2 + -3y

Simplifying
0 = -8x2 + -3y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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