((x^2)-(y^2))dx+(3xy)dy=0

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Solution for ((x^2)-(y^2))dx+(3xy)dy=0 equation: 


Simplifying
((x2) + -1(y2)) * dx + (3xy) * dy = 0
(x2 + -1(y2)) * dx + (3xy) * dy = 0

Reorder the terms for easier multiplication:
dx(x2 + -1y2) + (3xy) * dy = 0
(x2 * dx + -1y2 * dx) + (3xy) * dy = 0

Reorder the terms:
(-1dxy2 + dx3) + (3xy) * dy = 0
(-1dxy2 + dx3) + (3xy) * dy = 0

Remove parenthesis around (3xy)
-1dxy2 + dx3 + 3xy * dy = 0

Multiply xy * dy
-1dxy2 + dx3 + 3dxy2 = 0

Reorder the terms:
-1dxy2 + 3dxy2 + dx3 = 0

Combine like terms: -1dxy2 + 3dxy2 = 2dxy2
2dxy2 + dx3 = 0

Solving
2dxy2 + dx3 = 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), 'dx'.
dx(2y2 + x2) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(2y2 + x2)' equal to zero and attempt to solve:

Simplifying
2y2 + x2 = 0

Reorder the terms:
x2 + 2y2 = 0

Solving
x2 + 2y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 + 2y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 2y2 = 0 + -1x2
2y2 = 0 + -1x2
Remove the zero:
2y2 = -1x2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x2 + -2y2

Simplifying
0 = -1x2 + -2y2

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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