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

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


Simplifying
(4x4 + 4y) * dx + (4x + 4y2) * dy = 0

Reorder the terms for easier multiplication:
dx(4x4 + 4y) + (4x + 4y2) * dy = 0
(4x4 * dx + 4y * dx) + (4x + 4y2) * dy = 0

Reorder the terms:
(4dxy + 4dx5) + (4x + 4y2) * dy = 0
(4dxy + 4dx5) + (4x + 4y2) * dy = 0

Reorder the terms for easier multiplication:
4dxy + 4dx5 + dy(4x + 4y2) = 0
4dxy + 4dx5 + (4x * dy + 4y2 * dy) = 0
4dxy + 4dx5 + (4dxy + 4dy3) = 0

Reorder the terms:
4dxy + 4dxy + 4dx5 + 4dy3 = 0

Combine like terms: 4dxy + 4dxy = 8dxy
8dxy + 4dx5 + 4dy3 = 0

Solving
8dxy + 4dx5 + 4dy3 = 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), '4d'.
4d(2xy + x5 + y3) = 0

Ignore the factor 4.

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 + x5 + y3)' equal to zero and attempt to solve:

Simplifying
2xy + x5 + y3 = 0

Solving
2xy + x5 + y3 = 0

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

Add '-2xy' to each side of the equation.
2xy + x5 + -2xy + y3 = 0 + -2xy

Reorder the terms:
2xy + -2xy + x5 + y3 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x5 + y3 = 0 + -2xy
x5 + y3 = 0 + -2xy
Remove the zero:
x5 + y3 = -2xy

Add '-1x5' to each side of the equation.
x5 + -1x5 + y3 = -2xy + -1x5

Combine like terms: x5 + -1x5 = 0
0 + y3 = -2xy + -1x5
y3 = -2xy + -1x5

Add '-1y3' to each side of the equation.
y3 + -1y3 = -2xy + -1x5 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -2xy + -1x5 + -1y3

Simplifying
0 = -2xy + -1x5 + -1y3

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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