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

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


Simplifying
y2dx + (x + -2xy + -1y2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + dy(x + -2xy + -1y2) = 0
dxy2 + (x * dy + -2xy * dy + -1y2 * dy) = 0
dxy2 + (dxy + -2dxy2 + -1dy3) = 0

Reorder the terms:
dxy + dxy2 + -2dxy2 + -1dy3 = 0

Combine like terms: dxy2 + -2dxy2 = -1dxy2
dxy + -1dxy2 + -1dy3 = 0

Solving
dxy + -1dxy2 + -1dy3 = 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(x + -1xy + -1y2) = 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 '(x + -1xy + -1y2)' equal to zero and attempt to solve:

Simplifying
x + -1xy + -1y2 = 0

Solving
x + -1xy + -1y2 = 0

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

Add '-1x' to each side of the equation.
x + -1xy + -1x + -1y2 = 0 + -1x

Reorder the terms:
x + -1x + -1xy + -1y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + -1xy + -1y2 = 0 + -1x
-1xy + -1y2 = 0 + -1x
Remove the zero:
-1xy + -1y2 = -1x

Add 'xy' to each side of the equation.
-1xy + xy + -1y2 = -1x + xy

Combine like terms: -1xy + xy = 0
0 + -1y2 = -1x + xy
-1y2 = -1x + xy

Add 'y2' to each side of the equation.
-1y2 + y2 = -1x + xy + y2

Combine like terms: -1y2 + y2 = 0
0 = -1x + xy + y2

Simplifying
0 = -1x + xy + y2

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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