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I'm attempting to solve the recurrence relation

$$T_{(n)}=4T_{(nāˆ’1)}+(n+5) 3^n$$ with the conditions:

$n>0$
$T(0)=0$

I know the solution must be in the form $$T_{(n)}=T_h+T_p $$

but I think I'm making a mistake since when I calculate $T_h$ it gives me 0, and also don't know how to guess the $F_{(n)} = (n+5)*3^n$ int the non-homogeneous part.

user3120754
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  • So you just want it in the form of another recurrence? Not in closed form? Are there any constraints on what $h$ or $p$ should be? ā€“ ryan Nov 14 '17 at 05:43
  • Th is the solution to the homogeneous recurrence relation and Tp is the particular solution of the recurrence, but when I try to solve the homogeneous part ( T(n) = 4T(n-1) ), I get the equation X = 4. That leads to T(n) = c1*4^n, using the initial value T(0) = 0 the only value that satisfy the equation is c1 = 0, so the Th = 0, and i cant calculate the particular solution... ā€“ user3120754 Nov 14 '17 at 05:50
  • You can use a method that doesn't involve guessing. ā€“ Raphael Nov 14 '17 at 06:27

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