Xydx+(y^2-x^2)dy=0

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


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

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

Reorder the terms for easier multiplication:
dxyX + dy(-1x2 + y2) = 0
dxyX + (-1x2 * dy + y2 * dy) = 0
dxyX + (-1dx2y + dy3) = 0

Solving
dxyX + -1dx2y + dy3 = 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(xX + -1x2 + 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 '(xX + -1x2 + y2)' equal to zero and attempt to solve:

Simplifying
xX + -1x2 + y2 = 0

Solving
xX + -1x2 + y2 = 0

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

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

Reorder the terms:
xX + -1xX + -1x2 + y2 = 0 + -1xX

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

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

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

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

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

Simplifying
0 = -1xX + x2 + -1y2

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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