Substitution method for solving recurrences piece wise function I don't know how to use the substitution method for the following function: 
piece wise function:
$T(n) =  c$,  if $n=0$
$T(n) =  d$,  if $n=1$
$T(n)=2T(n-1)-T(n-2)+1$,  if $n > 1$

Let $T(n)=f(n)+an+b$ where $a,b$ are arbitrary constants
$$\implies f(m)+am+b=2[f(m-1)+a(m-1)+b]-[f(m-2)+a(m-2)+b]+1$$
$$\iff f(m)-2f(m-1)+f(m-2)=a+1$$
Set $a+1=0$ and use this
