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

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


Simplifying
(4x4 + 2y) * dx + (2x + 2y4) * dy = 0

Reorder the terms for easier multiplication:
dx(4x4 + 2y) + (2x + 2y4) * dy = 0
(4x4 * dx + 2y * dx) + (2x + 2y4) * dy = 0

Reorder the terms:
(2dxy + 4dx5) + (2x + 2y4) * dy = 0
(2dxy + 4dx5) + (2x + 2y4) * dy = 0

Reorder the terms for easier multiplication:
2dxy + 4dx5 + dy(2x + 2y4) = 0
2dxy + 4dx5 + (2x * dy + 2y4 * dy) = 0
2dxy + 4dx5 + (2dxy + 2dy5) = 0

Reorder the terms:
2dxy + 2dxy + 4dx5 + 2dy5 = 0

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + 4dx5 + 2dy5 = 0

Solving
4dxy + 4dx5 + 2dy5 = 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), '2d'.
2d(2xy + 2x5 + y5) = 0

Ignore the factor 2.

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 '(2xy + 2x5 + y5)' equal to zero and attempt to solve:

Simplifying
2xy + 2x5 + y5 = 0

Solving
2xy + 2x5 + y5 = 0

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

Add '-2xy' to each side of the equation.
2xy + 2x5 + -2xy + y5 = 0 + -2xy

Reorder the terms:
2xy + -2xy + 2x5 + y5 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 2x5 + y5 = 0 + -2xy
2x5 + y5 = 0 + -2xy
Remove the zero:
2x5 + y5 = -2xy

Add '-2x5' to each side of the equation.
2x5 + -2x5 + y5 = -2xy + -2x5

Combine like terms: 2x5 + -2x5 = 0
0 + y5 = -2xy + -2x5
y5 = -2xy + -2x5

Add '-1y5' to each side of the equation.
y5 + -1y5 = -2xy + -2x5 + -1y5

Combine like terms: y5 + -1y5 = 0
0 = -2xy + -2x5 + -1y5

Simplifying
0 = -2xy + -2x5 + -1y5

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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