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

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


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

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

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

Multiply xy * dy
-1dxy2 + dx3 = dxy2

Solving
-1dxy2 + dx3 = dxy2

Solving for variable 'd'.

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

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

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

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

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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