y(n-1)+0.5ny(n)=0.5(x+1)

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Solution for y(n-1)+0.5ny(n)=0.5(x+1) equation: 


Simplifying
y(n + -1) + 0.5ny(n) = 0.5(x + 1)

Reorder the terms:
y(-1 + n) + 0.5ny(n) = 0.5(x + 1)
(-1 * y + n * y) + 0.5ny(n) = 0.5(x + 1)

Reorder the terms:
(ny + -1y) + 0.5ny(n) = 0.5(x + 1)
(ny + -1y) + 0.5ny(n) = 0.5(x + 1)

Multiply ny * n
ny + -1y + 0.5n2y = 0.5(x + 1)

Reorder the terms:
ny + 0.5n2y + -1y = 0.5(x + 1)

Reorder the terms:
ny + 0.5n2y + -1y = 0.5(1 + x)
ny + 0.5n2y + -1y = (1 * 0.5 + x * 0.5)
ny + 0.5n2y + -1y = (0.5 + 0.5x)

Solving
ny + 0.5n2y + -1y = 0.5 + 0.5x

Solving for variable 'n'.

Reorder the terms:
-0.5 + ny + 0.5n2y + -0.5x + -1y = 0.5 + 0.5x + -0.5 + -0.5x

Reorder the terms:
-0.5 + ny + 0.5n2y + -0.5x + -1y = 0.5 + -0.5 + 0.5x + -0.5x

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + ny + 0.5n2y + -0.5x + -1y = 0.0 + 0.5x + -0.5x
-0.5 + ny + 0.5n2y + -0.5x + -1y = 0.5x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
-0.5 + ny + 0.5n2y + -0.5x + -1y = 0.0

The solution to this equation could not be determined.

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