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

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


Simplifying
(y2 + -1x2)(dx + xy) * dy = 0

Reorder the terms:
(-1x2 + y2)(dx + xy) * dy = 0

Reorder the terms for easier multiplication:
dy(-1x2 + y2)(dx + xy) = 0

Multiply (-1x2 + y2) * (dx + xy)
dy(-1x2 * (dx + xy) + y2(dx + xy)) = 0
dy((dx * -1x2 + xy * -1x2) + y2(dx + xy)) = 0
dy((-1dx3 + -1x3y) + y2(dx + xy)) = 0
dy(-1dx3 + -1x3y + (dx * y2 + xy * y2)) = 0
dy(-1dx3 + -1x3y + (dxy2 + xy3)) = 0

Reorder the terms:
dy(dxy2 + -1dx3 + xy3 + -1x3y) = 0
dy(dxy2 + -1dx3 + xy3 + -1x3y) = 0
(dxy2 * dy + -1dx3 * dy + xy3 * dy + -1x3y * dy) = 0

Reorder the terms:
(dxy4 + -1dx3y2 + d2xy3 + -1d2x3y) = 0
(dxy4 + -1dx3y2 + d2xy3 + -1d2x3y) = 0

Solving
dxy4 + -1dx3y2 + d2xy3 + -1d2x3y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'dxy'.
dxy(y3 + -1x2y + dy2 + -1dx2) = 0


Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve:

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(y3 + -1x2y + dy2 + -1dx2)' equal to zero and attempt to solve:

Simplifying
y3 + -1x2y + dy2 + -1dx2 = 0

Reorder the terms:
-1dx2 + dy2 + -1x2y + y3 = 0

Solving
-1dx2 + dy2 + -1x2y + y3 = 0

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

Add 'x2y' to each side of the equation.
-1dx2 + dy2 + -1x2y + x2y + y3 = 0 + x2y

Combine like terms: -1x2y + x2y = 0
-1dx2 + dy2 + 0 + y3 = 0 + x2y
-1dx2 + dy2 + y3 = 0 + x2y
Remove the zero:
-1dx2 + dy2 + y3 = x2y

Add '-1y3' to each side of the equation.
-1dx2 + dy2 + y3 + -1y3 = x2y + -1y3

Combine like terms: y3 + -1y3 = 0
-1dx2 + dy2 + 0 = x2y + -1y3
-1dx2 + dy2 = x2y + -1y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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