y(k)-0.75*y(k-1)+0.125*y(k-2)=e(k)

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Solution for y(k)-0.75*y(k-1)+0.125*y(k-2)=e(k) equation: 


Simplifying
y(k) + -0.75y(k + -1) + 0.125y(k + -2) = e(k)

Multiply y * k
ky + -0.75y(k + -1) + 0.125y(k + -2) = e(k)

Reorder the terms:
ky + -0.75y(-1 + k) + 0.125y(k + -2) = e(k)
ky + (-1 * -0.75y + k * -0.75y) + 0.125y(k + -2) = e(k)

Reorder the terms:
ky + (-0.75ky + 0.75y) + 0.125y(k + -2) = e(k)
ky + (-0.75ky + 0.75y) + 0.125y(k + -2) = e(k)

Reorder the terms:
ky + -0.75ky + 0.75y + 0.125y(-2 + k) = e(k)
ky + -0.75ky + 0.75y + (-2 * 0.125y + k * 0.125y) = e(k)

Reorder the terms:
ky + -0.75ky + 0.75y + (0.125ky + -0.25y) = e(k)
ky + -0.75ky + 0.75y + (0.125ky + -0.25y) = e(k)

Reorder the terms:
ky + -0.75ky + 0.125ky + 0.75y + -0.25y = e(k)

Combine like terms: ky + -0.75ky = 0.25ky
0.25ky + 0.125ky + 0.75y + -0.25y = e(k)

Combine like terms: 0.25ky + 0.125ky = 0.375ky
0.375ky + 0.75y + -0.25y = e(k)

Combine like terms: 0.75y + -0.25y = 0.5y
0.375ky + 0.5y = e(k)

Multiply e * k
0.375ky + 0.5y = ek

Solving
0.375ky + 0.5y = ek

Solving for variable 'k'.

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

Add '-1ek' to each side of the equation.
0.375ky + -1ek + 0.5y = ek + -1ek

Reorder the terms:
-1ek + 0.375ky + 0.5y = ek + -1ek

Combine like terms: ek + -1ek = 0
-1ek + 0.375ky + 0.5y = 0

Add '-0.5y' to each side of the equation.
-1ek + 0.375ky + 0.5y + -0.5y = 0 + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
-1ek + 0.375ky + 0.0 = 0 + -0.5y
-1ek + 0.375ky = 0 + -0.5y
Remove the zero:
-1ek + 0.375ky = -0.5y

Combine like terms: -0.5y + 0.5y = 0.0
-1ek + 0.375ky + 0.5y = 0.0

The solution to this equation could not be determined.

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