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

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


Simplifying
(Y2 + -1x2) * dy + (2xy) * dx = 0

Reorder the terms for easier multiplication:
dy(Y2 + -1x2) + (2xy) * dx = 0
(Y2 * dy + -1x2 * dy) + (2xy) * dx = 0

Reorder the terms:
(-1dx2y + dyY2) + (2xy) * dx = 0
(-1dx2y + dyY2) + (2xy) * dx = 0

Remove parenthesis around (2xy)
-1dx2y + dyY2 + 2xy * dx = 0

Multiply xy * dx
-1dx2y + dyY2 + 2dx2y = 0

Reorder the terms:
-1dx2y + 2dx2y + dyY2 = 0

Combine like terms: -1dx2y + 2dx2y = 1dx2y
1dx2y + dyY2 = 0

Solving
1dx2y + dyY2 = 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), 'dy'.
dy(x2 + Y2) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(x2 + Y2)' equal to zero and attempt to solve:

Simplifying
x2 + Y2 = 0

Reorder the terms:
Y2 + x2 = 0

Solving
Y2 + x2 = 0

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

Add '-1Y2' to each side of the equation.
Y2 + -1Y2 + x2 = 0 + -1Y2

Combine like terms: Y2 + -1Y2 = 0
0 + x2 = 0 + -1Y2
x2 = 0 + -1Y2
Remove the zero:
x2 = -1Y2

Add '-1x2' to each side of the equation.
x2 + -1x2 = -1Y2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -1Y2 + -1x2

Simplifying
0 = -1Y2 + -1x2

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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