# Differential equation 2nd order

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

Thanks!

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CompuChip
Homework Helper
For a), what happens when n = m?

For b), you have found a complete set of an. Where can you plug these in to get a solution?

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

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

most appreciated.

HallsofIvy
$$\sum_{m= 0}^\infty a_mx^{m+r}$$
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.