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

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


Simplifying
Ydy + (xy2 + -8x) * dx = 0

Reorder the terms:
dyY + (-8x + xy2) * dx = 0

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

Reorder the terms:
-8dx2 + dx2y2 + dyY = 0

Solving
-8dx2 + dx2y2 + dyY = 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(-8x2 + x2y2 + yY) = 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 '(-8x2 + x2y2 + yY)' equal to zero and attempt to solve:

Simplifying
-8x2 + x2y2 + yY = 0

Solving
-8x2 + x2y2 + yY = 0

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

Add '8x2' to each side of the equation.
-8x2 + x2y2 + 8x2 + yY = 0 + 8x2

Reorder the terms:
-8x2 + 8x2 + x2y2 + yY = 0 + 8x2

Combine like terms: -8x2 + 8x2 = 0
0 + x2y2 + yY = 0 + 8x2
x2y2 + yY = 0 + 8x2
Remove the zero:
x2y2 + yY = 8x2

Add '-1x2y2' to each side of the equation.
x2y2 + -1x2y2 + yY = 8x2 + -1x2y2

Combine like terms: x2y2 + -1x2y2 = 0
0 + yY = 8x2 + -1x2y2
yY = 8x2 + -1x2y2

Add '-1yY' to each side of the equation.
yY + -1yY = 8x2 + -1x2y2 + -1yY

Combine like terms: yY + -1yY = 0
0 = 8x2 + -1x2y2 + -1yY

Simplifying
0 = 8x2 + -1x2y2 + -1yY

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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