Y(n)-0.5y(n-1)+0.06Y(N-2)=(0.4)N-1U(N-1)

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Solution for Y(n)-0.5y(n-1)+0.06Y(N-2)=(0.4)N-1U(N-1) equation: 


Simplifying
Y(n) + -0.5y(n + -1) + 0.06Y(N + -2) = (0.4) * N + -1U(N + -1)

Multiply Y * n
nY + -0.5y(n + -1) + 0.06Y(N + -2) = (0.4) * N + -1U(N + -1)

Reorder the terms:
nY + -0.5y(-1 + n) + 0.06Y(N + -2) = (0.4) * N + -1U(N + -1)
nY + (-1 * -0.5y + n * -0.5y) + 0.06Y(N + -2) = (0.4) * N + -1U(N + -1)

Reorder the terms:
nY + (-0.5ny + 0.5y) + 0.06Y(N + -2) = (0.4) * N + -1U(N + -1)
nY + (-0.5ny + 0.5y) + 0.06Y(N + -2) = (0.4) * N + -1U(N + -1)

Reorder the terms:
nY + -0.5ny + 0.5y + 0.06Y(-2 + N) = (0.4) * N + -1U(N + -1)
nY + -0.5ny + 0.5y + (-2 * 0.06Y + N * 0.06Y) = (0.4) * N + -1U(N + -1)

Reorder the terms:
nY + -0.5ny + 0.5y + (0.06NY + -0.12Y) = (0.4) * N + -1U(N + -1)
nY + -0.5ny + 0.5y + (0.06NY + -0.12Y) = (0.4) * N + -1U(N + -1)

Reorder the terms:
0.06NY + -0.12Y + nY + -0.5ny + 0.5y = (0.4) * N + -1U(N + -1)

Reorder the terms:
0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.4N + -1U(-1 + N)
0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.4N + (-1 * -1U + N * -1U)

Reorder the terms:
0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.4N + (-1NU + 1U)
0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.4N + (-1NU + 1U)

Solving
0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.4N + -1NU + 1U

Solving for variable 'N'.

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

Add '-0.4N' to each side of the equation.
0.06NY + -0.12Y + nY + -0.5ny + -0.4N + 0.5y = 0.4N + -1NU + -0.4N + 1U

Reorder the terms:
-0.4N + 0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.4N + -1NU + -0.4N + 1U

Reorder the terms:
-0.4N + 0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.4N + -0.4N + -1NU + 1U

Combine like terms: 0.4N + -0.4N = 0.0
-0.4N + 0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0.0 + -1NU + 1U
-0.4N + 0.06NY + -0.12Y + nY + -0.5ny + 0.5y = -1NU + 1U

Add 'NU' to each side of the equation.
-0.4N + 0.06NY + -0.12Y + nY + -0.5ny + NU + 0.5y = -1NU + NU + 1U

Reorder the terms:
-0.4N + NU + 0.06NY + -0.12Y + nY + -0.5ny + 0.5y = -1NU + NU + 1U

Combine like terms: -1NU + NU = 0
-0.4N + NU + 0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 0 + 1U
-0.4N + NU + 0.06NY + -0.12Y + nY + -0.5ny + 0.5y = 1U

Add '0.12Y' to each side of the equation.
-0.4N + NU + 0.06NY + -0.12Y + nY + -0.5ny + 0.12Y + 0.5y = 1U + 0.12Y

Reorder the terms:
-0.4N + NU + 0.06NY + -0.12Y + 0.12Y + nY + -0.5ny + 0.5y = 1U + 0.12Y

Combine like terms: -0.12Y + 0.12Y = 0.00
-0.4N + NU + 0.06NY + 0.00 + nY + -0.5ny + 0.5y = 1U + 0.12Y
-0.4N + NU + 0.06NY + nY + -0.5ny + 0.5y = 1U + 0.12Y

Add '-1nY' to each side of the equation.
-0.4N + NU + 0.06NY + nY + -0.5ny + -1nY + 0.5y = 1U + 0.12Y + -1nY

Reorder the terms:
-0.4N + NU + 0.06NY + nY + -1nY + -0.5ny + 0.5y = 1U + 0.12Y + -1nY

Combine like terms: nY + -1nY = 0
-0.4N + NU + 0.06NY + 0 + -0.5ny + 0.5y = 1U + 0.12Y + -1nY
-0.4N + NU + 0.06NY + -0.5ny + 0.5y = 1U + 0.12Y + -1nY

Add '0.5ny' to each side of the equation.
-0.4N + NU + 0.06NY + -0.5ny + 0.5ny + 0.5y = 1U + 0.12Y + -1nY + 0.5ny

Combine like terms: -0.5ny + 0.5ny = 0.0
-0.4N + NU + 0.06NY + 0.0 + 0.5y = 1U + 0.12Y + -1nY + 0.5ny
-0.4N + NU + 0.06NY + 0.5y = 1U + 0.12Y + -1nY + 0.5ny

Add '-0.5y' to each side of the equation.
-0.4N + NU + 0.06NY + 0.5y + -0.5y = 1U + 0.12Y + -1nY + 0.5ny + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
-0.4N + NU + 0.06NY + 0.0 = 1U + 0.12Y + -1nY + 0.5ny + -0.5y
-0.4N + NU + 0.06NY = 1U + 0.12Y + -1nY + 0.5ny + -0.5y

Reorder the terms:
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 1U + -1U + 0.12Y + -0.12Y + -1nY + nY + 0.5ny + -0.5ny + -0.5y + 0.5y

Combine like terms: 1U + -1U = 0
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 0 + 0.12Y + -0.12Y + -1nY + nY + 0.5ny + -0.5ny + -0.5y + 0.5y
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 0.12Y + -0.12Y + -1nY + nY + 0.5ny + -0.5ny + -0.5y + 0.5y

Combine like terms: 0.12Y + -0.12Y = 0.00
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 0.00 + -1nY + nY + 0.5ny + -0.5ny + -0.5y + 0.5y
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = -1nY + nY + 0.5ny + -0.5ny + -0.5y + 0.5y

Combine like terms: -1nY + nY = 0
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 0 + 0.5ny + -0.5ny + -0.5y + 0.5y
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 0.5ny + -0.5ny + -0.5y + 0.5y

Combine like terms: 0.5ny + -0.5ny = 0.0
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 0.0 + -0.5y + 0.5y
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = -0.5y + 0.5y

Combine like terms: -0.5y + 0.5y = 0.0
-0.4N + NU + 0.06NY + -1U + -0.12Y + nY + -0.5ny + 0.5y = 0.0

The solution to this equation could not be determined.

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