(5y+4x)dy+(4y-8x^3)dx=0

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Solution for (5y+4x)dy+(4y-8x^3)dx=0 equation: 


Simplifying
(5y + 4x) * dy + (4y + -8x3) * dx = 0

Reorder the terms:
(4x + 5y) * dy + (4y + -8x3) * dx = 0

Reorder the terms for easier multiplication:
dy(4x + 5y) + (4y + -8x3) * dx = 0
(4x * dy + 5y * dy) + (4y + -8x3) * dx = 0
(4dxy + 5dy2) + (4y + -8x3) * dx = 0

Reorder the terms:
4dxy + 5dy2 + (-8x3 + 4y) * dx = 0

Reorder the terms for easier multiplication:
4dxy + 5dy2 + dx(-8x3 + 4y) = 0
4dxy + 5dy2 + (-8x3 * dx + 4y * dx) = 0

Reorder the terms:
4dxy + 5dy2 + (4dxy + -8dx4) = 0
4dxy + 5dy2 + (4dxy + -8dx4) = 0

Reorder the terms:
4dxy + 4dxy + -8dx4 + 5dy2 = 0

Combine like terms: 4dxy + 4dxy = 8dxy
8dxy + -8dx4 + 5dy2 = 0

Solving
8dxy + -8dx4 + 5dy2 = 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(8xy + -8x4 + 5y2) = 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 '(8xy + -8x4 + 5y2)' equal to zero and attempt to solve:

Simplifying
8xy + -8x4 + 5y2 = 0

Solving
8xy + -8x4 + 5y2 = 0

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

Add '-8xy' to each side of the equation.
8xy + -8x4 + -8xy + 5y2 = 0 + -8xy

Reorder the terms:
8xy + -8xy + -8x4 + 5y2 = 0 + -8xy

Combine like terms: 8xy + -8xy = 0
0 + -8x4 + 5y2 = 0 + -8xy
-8x4 + 5y2 = 0 + -8xy
Remove the zero:
-8x4 + 5y2 = -8xy

Add '8x4' to each side of the equation.
-8x4 + 8x4 + 5y2 = -8xy + 8x4

Combine like terms: -8x4 + 8x4 = 0
0 + 5y2 = -8xy + 8x4
5y2 = -8xy + 8x4

Add '-5y2' to each side of the equation.
5y2 + -5y2 = -8xy + 8x4 + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = -8xy + 8x4 + -5y2

Simplifying
0 = -8xy + 8x4 + -5y2

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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