Differential equation 2nd order

[gomes.]

i managed to get the indicial equation/recurrence relation, but for parts (a) and (b), I am stuck. i got a0,a1,a2,a3... for part b, but how do i get the polynomial solution?

Thanks!

 

[CompuChip]

For a), what happens when n = m?

For b), you have found a complete set of a_n. Where can you plug these into get a solution?

 

[gomes.]

thanks, for (a), when n=m, the recurrence relation becomes 0? what would i do next? sorry I am still stuck

(b)sorry, i think my lecture notes missed out on this, what series/formula do i plug it into?

most appreciated.

 

[HallsofIvy]

You have your solution written as
\sum_{m= 0}^\infty a_mx^{m+r}
That is what you plug your "a_m" into. Notice that each a is a multiple of the one before it so if a_n= 0 for any n, all successive coefficients are 0 and your infinite sum becomes a polynomial as the problem says.