How to solve this difference equation using Laplace transformation?

214 Views Asked by At

My goal is to solve this difference equeation using laplace transformation. $$y[n] - 0.25y[n-1] = 2*\delta[n]\ \ n\in N$$

Note that $\delta[n] = 1$ if n= 0 and $\delta[n] = 0$ otherwise.

Taking laplace transformation on both sides of the equation, I got

$$Y(s) - 0.25 e^{-s}Y(s)= 2$$

Then, I have

$$ Y(s) = \dfrac{2}{ (1 - 0.25 * e^{-s}) }$$.

I know that the next step is taking the inverse Laplace transformation of Y(s), but how should I do that?