I have a question like this $y[n] - \frac 2 5y[n-1] = 2x[n]$ and $x[n] = 2u[n]$, the manual say that $y^p[n] = k u[n]$ and subtitute it into the equation will become $ k - \frac 25k = 4$. But I think that it should be $ ku[n] - \frac 25ku[n-1] = 4u[n]$, and I don't know how to solve it.
My question is why the u[n] disappear and how to solve it? If I change the input to delta, the method is the same?
Thx in advance.
x[n] is input signal and y[n] is output signal, u[n] is unit step function that u[n] = 1, n>=0, u[n] = 0, otherwise.