Help solve recurrence : f(x) = 2f(x-1) + x While trying to analyze the time complexity of the heapify algorithm ,
I came up with the following recurrence for it's time complexity in terms of heap height:

T(h) = 2T(h-1) + h 


Could you help me approach this recurrence?
To solve the recurrence $$a_h=2a_{h-1}+h \tag{1}$$ write $$b_h=a_h+h$$ Adding $h$ to both sides of $(1)$ gives $$b_h=2b_{h-1}+2$$  Can you take it from here?
$T(h)=2T(h-1)+h=2(2T(h-2)+(h-1))+h=2^2(2T(h-3)+(h-2))+2(h-1)+h$
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so you get:
$$T(h)= \Sigma_{i=0}^h2^i*(h-i)$$