(24x^2y+2xy+8y^3)dx+(x^2+y^2)dy=0

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Solution for (24x^2y+2xy+8y^3)dx+(x^2+y^2)dy=0 equation: 


Simplifying
(24x2y + 2xy + 8y3) * dx + (x2 + y2) * dy = 0

Reorder the terms:
(2xy + 24x2y + 8y3) * dx + (x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + 24x2y + 8y3) + (x2 + y2) * dy = 0
(2xy * dx + 24x2y * dx + 8y3 * dx) + (x2 + y2) * dy = 0

Reorder the terms:
(8dxy3 + 2dx2y + 24dx3y) + (x2 + y2) * dy = 0
(8dxy3 + 2dx2y + 24dx3y) + (x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
8dxy3 + 2dx2y + 24dx3y + dy(x2 + y2) = 0
8dxy3 + 2dx2y + 24dx3y + (x2 * dy + y2 * dy) = 0
8dxy3 + 2dx2y + 24dx3y + (dx2y + dy3) = 0

Reorder the terms:
8dxy3 + 2dx2y + dx2y + 24dx3y + dy3 = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
8dxy3 + 3dx2y + 24dx3y + dy3 = 0

Solving
8dxy3 + 3dx2y + 24dx3y + dy3 = 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), 'dy'.
dy(8xy2 + 3x2 + 24x3 + y2) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(8xy2 + 3x2 + 24x3 + y2)' equal to zero and attempt to solve:

Simplifying
8xy2 + 3x2 + 24x3 + y2 = 0

Solving
8xy2 + 3x2 + 24x3 + y2 = 0

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

Add '-8xy2' to each side of the equation.
8xy2 + 3x2 + 24x3 + -8xy2 + y2 = 0 + -8xy2

Reorder the terms:
8xy2 + -8xy2 + 3x2 + 24x3 + y2 = 0 + -8xy2

Combine like terms: 8xy2 + -8xy2 = 0
0 + 3x2 + 24x3 + y2 = 0 + -8xy2
3x2 + 24x3 + y2 = 0 + -8xy2
Remove the zero:
3x2 + 24x3 + y2 = -8xy2

Add '-3x2' to each side of the equation.
3x2 + 24x3 + -3x2 + y2 = -8xy2 + -3x2

Reorder the terms:
3x2 + -3x2 + 24x3 + y2 = -8xy2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 24x3 + y2 = -8xy2 + -3x2
24x3 + y2 = -8xy2 + -3x2

Add '-24x3' to each side of the equation.
24x3 + -24x3 + y2 = -8xy2 + -3x2 + -24x3

Combine like terms: 24x3 + -24x3 = 0
0 + y2 = -8xy2 + -3x2 + -24x3
y2 = -8xy2 + -3x2 + -24x3

Add '-1y2' to each side of the equation.
y2 + -1y2 = -8xy2 + -3x2 + -24x3 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -8xy2 + -3x2 + -24x3 + -1y2

Simplifying
0 = -8xy2 + -3x2 + -24x3 + -1y2

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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