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

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


Simplifying
(x + -2y) * dy + (2x + y) * dy = 0

Reorder the terms for easier multiplication:
dy(x + -2y) + (2x + y) * dy = 0
(x * dy + -2y * dy) + (2x + y) * dy = 0
(dxy + -2dy2) + (2x + y) * dy = 0

Reorder the terms for easier multiplication:
dxy + -2dy2 + dy(2x + y) = 0
dxy + -2dy2 + (2x * dy + y * dy) = 0
dxy + -2dy2 + (2dxy + dy2) = 0

Reorder the terms:
dxy + 2dxy + -2dy2 + dy2 = 0

Combine like terms: dxy + 2dxy = 3dxy
3dxy + -2dy2 + dy2 = 0

Combine like terms: -2dy2 + dy2 = -1dy2
3dxy + -1dy2 = 0

Solving
3dxy + -1dy2 = 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(3x + -1y) = 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 '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add '-3x' to each side of the equation.
3x + -3x + -1y = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + -1y = 0 + -3x
-1y = 0 + -3x
Remove the zero:
-1y = -3x

Add 'y' to each side of the equation.
-1y + y = -3x + y

Combine like terms: -1y + y = 0
0 = -3x + y

Simplifying
0 = -3x + y

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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