y(k+2)=0.25*y(k)

Solution for y(k+2)=0.25*y(k) equation:

Simplifying
y(k + 2) = 0.25y(k)

Reorder the terms:
y(2 + k) = 0.25y(k)
(2 * y + k * y) = 0.25y(k)

Reorder the terms:
(ky + 2y) = 0.25y(k)
(ky + 2y) = 0.25y(k)

Multiply y * k
ky + 2y = 0.25ky

Solving
ky + 2y = 0.25ky

Solving for variable 'k'.

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

Add '-0.25ky' to each side of the equation.
ky + -0.25ky + 2y = 0.25ky + -0.25ky

Combine like terms: ky + -0.25ky = 0.75ky
0.75ky + 2y = 0.25ky + -0.25ky

Combine like terms: 0.25ky + -0.25ky = 0.00
0.75ky + 2y = 0.00

Add '-2y' to each side of the equation.
0.75ky + 2y + -2y = 0.00 + -2y

Combine like terms: 2y + -2y = 0
0.75ky + 0 = 0.00 + -2y
0.75ky = 0.00 + -2y
Remove the zero:
0.75ky = -2y

Divide each side by '0.75y'.
k = -2.666666667

Simplifying
k = -2.666666667