y(n)=0.25y(n-2)+x(n)

Solution for y(n)=0.25y(n-2)+x(n) equation:

Simplifying
y(n) = 0.25y(n + -2) + x(n)

Multiply y * n
ny = 0.25y(n + -2) + x(n)

Reorder the terms:
ny = 0.25y(-2 + n) + x(n)
ny = (-2 * 0.25y + n * 0.25y) + x(n)

Reorder the terms:
ny = (0.25ny + -0.5y) + x(n)
ny = (0.25ny + -0.5y) + x(n)

Multiply x * n
ny = 0.25ny + -0.5y + nx

Reorder the terms:
ny = nx + 0.25ny + -0.5y

Solving
ny = nx + 0.25ny + -0.5y

Solving for variable 'n'.

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

Add '-1nx' to each side of the equation.
-1nx + ny = nx + 0.25ny + -1nx + -0.5y

Reorder the terms:
-1nx + ny = nx + -1nx + 0.25ny + -0.5y

Combine like terms: nx + -1nx = 0
-1nx + ny = 0 + 0.25ny + -0.5y
-1nx + ny = 0.25ny + -0.5y

Add '-0.25ny' to each side of the equation.
-1nx + ny + -0.25ny = 0.25ny + -0.25ny + -0.5y

Combine like terms: ny + -0.25ny = 0.75ny
-1nx + 0.75ny = 0.25ny + -0.25ny + -0.5y

Combine like terms: 0.25ny + -0.25ny = 0.00
-1nx + 0.75ny = 0.00 + -0.5y
-1nx + 0.75ny = -0.5y

Combine like terms: -0.5y + 0.5y = 0.0
-1nx + 0.75ny + 0.5y = 0.0

The solution to this equation could not be determined.