(x(1-y^2))dx+(Y(8-x^2))dy=0

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Solution for (x(1-y^2))dx+(Y(8-x^2))dy=0 equation: 


Simplifying
(x(1 + -1y2)) * dx + (Y(8 + -1x2)) * dy = 0
((1 * x + -1y2 * x)) * dx + (Y(8 + -1x2)) * dy = 0
((1x + -1xy2)) * dx + (Y(8 + -1x2)) * dy = 0

Reorder the terms for easier multiplication:
dx(1x + -1xy2) + (Y(8 + -1x2)) * dy = 0
(1x * dx + -1xy2 * dx) + (Y(8 + -1x2)) * dy = 0
(1dx2 + -1dx2y2) + (Y(8 + -1x2)) * dy = 0
1dx2 + -1dx2y2 + ((8 * Y + -1x2 * Y)) * dy = 0
1dx2 + -1dx2y2 + ((8Y + -1x2Y)) * dy = 0

Reorder the terms for easier multiplication:
1dx2 + -1dx2y2 + dy(8Y + -1x2Y) = 0
1dx2 + -1dx2y2 + (8Y * dy + -1x2Y * dy) = 0

Reorder the terms:
1dx2 + -1dx2y2 + (-1dx2yY + 8dyY) = 0
1dx2 + -1dx2y2 + (-1dx2yY + 8dyY) = 0

Reorder the terms:
1dx2 + -1dx2yY + -1dx2y2 + 8dyY = 0

Solving
1dx2 + -1dx2yY + -1dx2y2 + 8dyY = 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 + -1x2yY + -1x2y2 + 8yY) = 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 + -1x2yY + -1x2y2 + 8yY)' equal to zero and attempt to solve:

Simplifying
x2 + -1x2yY + -1x2y2 + 8yY = 0

Solving
x2 + -1x2yY + -1x2y2 + 8yY = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2yY + -1x2y2 + -1x2 + 8yY = 0 + -1x2

Reorder the terms:
x2 + -1x2 + -1x2yY + -1x2y2 + 8yY = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -1x2yY + -1x2y2 + 8yY = 0 + -1x2
-1x2yY + -1x2y2 + 8yY = 0 + -1x2
Remove the zero:
-1x2yY + -1x2y2 + 8yY = -1x2

Add 'x2yY' to each side of the equation.
-1x2yY + -1x2y2 + x2yY + 8yY = -1x2 + x2yY

Reorder the terms:
-1x2yY + x2yY + -1x2y2 + 8yY = -1x2 + x2yY

Combine like terms: -1x2yY + x2yY = 0
0 + -1x2y2 + 8yY = -1x2 + x2yY
-1x2y2 + 8yY = -1x2 + x2yY

Add 'x2y2' to each side of the equation.
-1x2y2 + x2y2 + 8yY = -1x2 + x2yY + x2y2

Combine like terms: -1x2y2 + x2y2 = 0
0 + 8yY = -1x2 + x2yY + x2y2
8yY = -1x2 + x2yY + x2y2

Add '-8yY' to each side of the equation.
8yY + -8yY = -1x2 + x2yY + x2y2 + -8yY

Combine like terms: 8yY + -8yY = 0
0 = -1x2 + x2yY + x2y2 + -8yY

Simplifying
0 = -1x2 + x2yY + x2y2 + -8yY

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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