Question

How do you know how many initial conditions are there when I want to find the impulse response say of 8y[n]+6y[n-1]=x[n]?

Answer 1

I know for this we just check for when n=0 but say for 5y[n]+2y[n-1]-3y[n-2]=x[n] you check at the instance when n=0, AND when n=1 how come?

Answer 2

how do you know what equations require you to check for n=1, and how about even further such as n=2.. etc?