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

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


Simplifying
(y + -1x5) * dx + (x + y5) * dy = 0

Reorder the terms:
(-1x5 + y) * dx + (x + y5) * dy = 0

Reorder the terms for easier multiplication:
dx(-1x5 + y) + (x + y5) * dy = 0
(-1x5 * dx + y * dx) + (x + y5) * dy = 0

Reorder the terms:
(dxy + -1dx6) + (x + y5) * dy = 0
(dxy + -1dx6) + (x + y5) * dy = 0

Reorder the terms for easier multiplication:
dxy + -1dx6 + dy(x + y5) = 0
dxy + -1dx6 + (x * dy + y5 * dy) = 0
dxy + -1dx6 + (dxy + dy6) = 0

Reorder the terms:
dxy + dxy + -1dx6 + dy6 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + -1dx6 + dy6 = 0

Solving
2dxy + -1dx6 + dy6 = 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(2xy + -1x6 + y6) = 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 '(2xy + -1x6 + y6)' equal to zero and attempt to solve:

Simplifying
2xy + -1x6 + y6 = 0

Solving
2xy + -1x6 + y6 = 0

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

Add '-2xy' to each side of the equation.
2xy + -1x6 + -2xy + y6 = 0 + -2xy

Reorder the terms:
2xy + -2xy + -1x6 + y6 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + -1x6 + y6 = 0 + -2xy
-1x6 + y6 = 0 + -2xy
Remove the zero:
-1x6 + y6 = -2xy

Add 'x6' to each side of the equation.
-1x6 + x6 + y6 = -2xy + x6

Combine like terms: -1x6 + x6 = 0
0 + y6 = -2xy + x6
y6 = -2xy + x6

Add '-1y6' to each side of the equation.
y6 + -1y6 = -2xy + x6 + -1y6

Combine like terms: y6 + -1y6 = 0
0 = -2xy + x6 + -1y6

Simplifying
0 = -2xy + x6 + -1y6

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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