(8y-x^2y)dy+(x+xy^2)dx=0

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Solution for (8y-x^2y)dy+(x+xy^2)dx=0 equation: 


Simplifying
(8y + -1x2y) * dy + (x + xy2) * dx = 0

Reorder the terms:
(-1x2y + 8y) * dy + (x + xy2) * dx = 0

Reorder the terms for easier multiplication:
dy(-1x2y + 8y) + (x + xy2) * dx = 0
(-1x2y * dy + 8y * dy) + (x + xy2) * dx = 0
(-1dx2y2 + 8dy2) + (x + xy2) * dx = 0

Reorder the terms for easier multiplication:
-1dx2y2 + 8dy2 + dx(x + xy2) = 0
-1dx2y2 + 8dy2 + (x * dx + xy2 * dx) = 0
-1dx2y2 + 8dy2 + (dx2 + dx2y2) = 0

Reorder the terms:
dx2 + -1dx2y2 + dx2y2 + 8dy2 = 0

Combine like terms: -1dx2y2 + dx2y2 = 0
dx2 + 0 + 8dy2 = 0
dx2 + 8dy2 = 0

Solving
dx2 + 8dy2 = 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(x2 + 8y2) = 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 '(x2 + 8y2)' equal to zero and attempt to solve:

Simplifying
x2 + 8y2 = 0

Solving
x2 + 8y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 + 8y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 8y2 = 0 + -1x2
8y2 = 0 + -1x2
Remove the zero:
8y2 = -1x2

Add '-8y2' to each side of the equation.
8y2 + -8y2 = -1x2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
0 = -1x2 + -8y2

Simplifying
0 = -1x2 + -8y2

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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