Rojas Barker
03/26/2023 · High School
1. (10 Puntos) Resolver la siguiente ecuación en diferencias usando la transformada Z. \[ \begin{array}{l}x(n+3)-4 \cdot x(n+1)=3^{n} \\ x(0)=1 \\ x(1)=2 \\ x(1)=3\end{array} \]
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Para resolver la ecuación en diferencias usando la transformada Z, se aplica la transformada Z a la ecuación y se utilizan los valores iniciales para obtener la expresión de \(X(z)\). Luego, se realiza la inversa de la transformada Z para obtener la solución \(x(n)\). La expresión de \(X(z)\) es:
\[
X(z) = \frac{z^4 - z^3 - 3z^2 - 8z + 12}{(z^3 - 4z)(z - 3)}
\]
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