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

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


Simplifying
(y2 + -1x2) * dx + 2xy = 0

Reorder the terms:
(-1x2 + y2) * dx + 2xy = 0

Reorder the terms for easier multiplication:
dx(-1x2 + y2) + 2xy = 0
(-1x2 * dx + y2 * dx) + 2xy = 0

Reorder the terms:
(dxy2 + -1dx3) + 2xy = 0
(dxy2 + -1dx3) + 2xy = 0

Solving
dxy2 + -1dx3 + 2xy = 0

Solving for variable 'd'.

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

Add '-2xy' to each side of the equation.
dxy2 + -1dx3 + 2xy + -2xy = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
dxy2 + -1dx3 + 0 = 0 + -2xy
dxy2 + -1dx3 = 0 + -2xy
Remove the zero:
dxy2 + -1dx3 = -2xy

Combine like terms: -2xy + 2xy = 0
dxy2 + -1dx3 + 2xy = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(dy2 + -1dx2 + 2y) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

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 '(dy2 + -1dx2 + 2y)' equal to zero and attempt to solve:

Simplifying
dy2 + -1dx2 + 2y = 0

Reorder the terms:
-1dx2 + dy2 + 2y = 0

Solving
-1dx2 + dy2 + 2y = 0

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

Add '-2y' to each side of the equation.
-1dx2 + dy2 + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1dx2 + dy2 + 0 = 0 + -2y
-1dx2 + dy2 = 0 + -2y
Remove the zero:
-1dx2 + dy2 = -2y

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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