non homogeneous linear recursion

**guyonfire89** · Dec 5th 2010, 09:43 PM

I have a problem that says

Find an explicit formula for an if a0=0 and an+1=an+2^n

Can I convert this equation to

an=-an+1-2^n?
then keep solving as if it were a non-homogeneous equation?

Sorry for my lack of use of latex.

**hmmmm** · Dec 5th 2010, 11:59 PM

No you need to find the solution to the homogeneous equation (take away 2^n) then try to find a particular solution (try $c*2^n$ ) and then add these two together. Once you have do this all you need to do is solve for the initial conditions, it's just like solving a linear non-homogeneous 1st-order differential equation,

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