(y^2)dx+(x*y-1)dy=0

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Solution for (y^2)dx+(x*y-1)dy=0 equation: 


Simplifying
(y2) * dx + (x * y + -1) * dy = 0

Multiply y2 * dx
dxy2 + (x * y + -1) * dy = 0

Multiply x * y
dxy2 + (xy + -1) * dy = 0

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

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

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

Combine like terms: dxy2 + dxy2 = 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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