y^1=xy^2

Solution for y^1=xy^2 equation:

Simplifying
y = xy2

Solving
y = xy2

Solving for variable 'y'.

Reorder the terms:
-1xy2 + y = xy2 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
-1xy2 + y = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1xy + 1) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-1xy + 1)' equal to zero and attempt to solve:

Simplifying
-1xy + 1 = 0

Reorder the terms:
1 + -1xy = 0

Solving
1 + -1xy = 0

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

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

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

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

Divide each side by '-1x'.
y = x-1

Simplifying
y = x-1
Solution
y = {0, x-1}