(2*y^3*x+4)*dx+(3*y^2*x^2+8)*dy=0

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Solution for (2*y^3*x+4)*dx+(3*y^2*x^2+8)*dy=0 equation: 


Simplifying
(2y3 * x + 4) * dx + (3y2 * x2 + 8) * dy = 0

Multiply y3 * x
(2xy3 + 4) * dx + (3y2 * x2 + 8) * dy = 0

Reorder the terms:
(4 + 2xy3) * dx + (3y2 * x2 + 8) * dy = 0

Reorder the terms for easier multiplication:
dx(4 + 2xy3) + (3y2 * x2 + 8) * dy = 0
(4 * dx + 2xy3 * dx) + (3y2 * x2 + 8) * dy = 0
(4dx + 2dx2y3) + (3y2 * x2 + 8) * dy = 0

Multiply y2 * x2
4dx + 2dx2y3 + (3x2y2 + 8) * dy = 0

Reorder the terms:
4dx + 2dx2y3 + (8 + 3x2y2) * dy = 0

Reorder the terms for easier multiplication:
4dx + 2dx2y3 + dy(8 + 3x2y2) = 0
4dx + 2dx2y3 + (8 * dy + 3x2y2 * dy) = 0

Reorder the terms:
4dx + 2dx2y3 + (3dx2y3 + 8dy) = 0
4dx + 2dx2y3 + (3dx2y3 + 8dy) = 0

Combine like terms: 2dx2y3 + 3dx2y3 = 5dx2y3
4dx + 5dx2y3 + 8dy = 0

Solving
4dx + 5dx2y3 + 8dy = 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(4x + 5x2y3 + 8y) = 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 '(4x + 5x2y3 + 8y)' equal to zero and attempt to solve:

Simplifying
4x + 5x2y3 + 8y = 0

Solving
4x + 5x2y3 + 8y = 0

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

Add '-4x' to each side of the equation.
4x + 5x2y3 + -4x + 8y = 0 + -4x

Reorder the terms:
4x + -4x + 5x2y3 + 8y = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + 5x2y3 + 8y = 0 + -4x
5x2y3 + 8y = 0 + -4x
Remove the zero:
5x2y3 + 8y = -4x

Add '-5x2y3' to each side of the equation.
5x2y3 + -5x2y3 + 8y = -4x + -5x2y3

Combine like terms: 5x2y3 + -5x2y3 = 0
0 + 8y = -4x + -5x2y3
8y = -4x + -5x2y3

Add '-8y' to each side of the equation.
8y + -8y = -4x + -5x2y3 + -8y

Combine like terms: 8y + -8y = 0
0 = -4x + -5x2y3 + -8y

Simplifying
0 = -4x + -5x2y3 + -8y

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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