(2y-1)dx+xdy=0

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Solution for (2y-1)dx+xdy=0 equation: 


Simplifying
(2y + -1) * dx + xdy = 0

Reorder the terms:
(-1 + 2y) * dx + xdy = 0

Reorder the terms for easier multiplication:
dx(-1 + 2y) + xdy = 0
(-1 * dx + 2y * dx) + xdy = 0
(-1dx + 2dxy) + xdy = 0

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

Solving
-1dx + 3dxy = 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), 'dx'.
dx(-1 + 3y) = 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 '(-1 + 3y)' equal to zero and attempt to solve:

Simplifying
-1 + 3y = 0

Solving
-1 + 3y = 0

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

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

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

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

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

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

Simplifying
0 = 1 + -3y

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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