y^2dx-(3xy-1)dy=0

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Solution for y^2dx-(3xy-1)dy=0 equation: 


Simplifying
y2dx + -1(3xy + -1) * dy = 0

Reorder the terms:
dxy2 + -1(-1 + 3xy) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + -1dy(-1 + 3xy) = 0
dxy2 + (-1 * -1dy + 3xy * -1dy) = 0

Reorder the terms:
dxy2 + (-3dxy2 + 1dy) = 0
dxy2 + (-3dxy2 + 1dy) = 0

Combine like terms: dxy2 + -3dxy2 = -2dxy2
-2dxy2 + 1dy = 0

Solving
-2dxy2 + 1dy = 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(-2xy + 1) = 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 '(-2xy + 1)' equal to zero and attempt to solve:

Simplifying
-2xy + 1 = 0

Reorder the terms:
1 + -2xy = 0

Solving
1 + -2xy = 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 + -2xy = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2xy = 0 + -1
-2xy = 0 + -1

Combine like terms: 0 + -1 = -1
-2xy = -1

Add '2xy' to each side of the equation.
-2xy + 2xy = -1 + 2xy

Combine like terms: -2xy + 2xy = 0
0 = -1 + 2xy

Simplifying
0 = -1 + 2xy

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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