y(n)+y(n-2)=2x(n)-x(n-1)

Solution for y(n)+y(n-2)=2x(n)-x(n-1) equation:

Simplifying
y(n) + y(n + -2) = 2x(n) + -1x(n + -1)

Multiply y * n
ny + y(n + -2) = 2x(n) + -1x(n + -1)

Reorder the terms:
ny + y(-2 + n) = 2x(n) + -1x(n + -1)
ny + (-2 * y + n * y) = 2x(n) + -1x(n + -1)

Reorder the terms:
ny + (ny + -2y) = 2x(n) + -1x(n + -1)
ny + (ny + -2y) = 2x(n) + -1x(n + -1)

Combine like terms: ny + ny = 2ny
2ny + -2y = 2x(n) + -1x(n + -1)

Multiply x * n
2ny + -2y = 2nx + -1x(n + -1)

Reorder the terms:
2ny + -2y = 2nx + -1x(-1 + n)
2ny + -2y = 2nx + (-1 * -1x + n * -1x)

Reorder the terms:
2ny + -2y = 2nx + (-1nx + 1x)
2ny + -2y = 2nx + (-1nx + 1x)

Combine like terms: 2nx + -1nx = 1nx
2ny + -2y = 1nx + 1x

Solving
2ny + -2y = 1nx + 1x

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.
2ny + -1nx + -2y = 1nx + -1nx + 1x

Reorder the terms:
-1nx + 2ny + -2y = 1nx + -1nx + 1x

Combine like terms: 1nx + -1nx = 0
-1nx + 2ny + -2y = 0 + 1x
-1nx + 2ny + -2y = 1x

Add '2y' to each side of the equation.
-1nx + 2ny + -2y + 2y = 1x + 2y

Combine like terms: -2y + 2y = 0
-1nx + 2ny + 0 = 1x + 2y
-1nx + 2ny = 1x + 2y

Reorder the terms:
-1nx + 2ny + -1x + -2y = 1x + -1x + 2y + -2y

Combine like terms: 1x + -1x = 0
-1nx + 2ny + -1x + -2y = 0 + 2y + -2y
-1nx + 2ny + -1x + -2y = 2y + -2y

Combine like terms: 2y + -2y = 0
-1nx + 2ny + -1x + -2y = 0

The solution to this equation could not be determined.