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

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


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

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

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

Reorder the terms:
(-1dxy2 + dx2y + dx3) + (xy) * dy = 0
(-1dxy2 + dx2y + dx3) + (xy) * dy = 0

Multiply xy * dy
-1dxy2 + dx2y + dx3 + dxy2 = 0

Reorder the terms:
-1dxy2 + dxy2 + dx2y + dx3 = 0

Combine like terms: -1dxy2 + dxy2 = 0
0 + dx2y + dx3 = 0
dx2y + dx3 = 0

Solving
dx2y + 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), 'dx2'.
dx2(y + x) = 0


Subproblem 1
Set the factor 'dx2' equal to zero and attempt to solve:

Simplifying
dx2 = 0

Solving
dx2 = 0

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

Simplifying
dx2 = 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 '(y + x)' equal to zero and attempt to solve:

Simplifying
y + x = 0

Reorder the terms:
x + y = 0

Solving
x + y = 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 + y = 0 + -1x

Combine like terms: x + -1x = 0
0 + y = 0 + -1x
y = 0 + -1x
Remove the zero:
y = -1x

Add '-1y' to each side of the equation.
y + -1y = -1x + -1y

Combine like terms: y + -1y = 0
0 = -1x + -1y

Simplifying
0 = -1x + -1y

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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