ODE question to follow......

Question

seascorpion1 · Answer

I have a power series substitution which I need to simplify to $$L[y(x,r)]=x^r(r-r_1)^2$$I've got as far as$$L[y(x,r)]=\sum_{n=0}^{\infty}(c_n(r)(n+r)(n+r-1)+\sum_{k=0}^{n}(p_{n-k}(k+r)+q_{n-k})c_k(r))x^{n+r}$$Can anyone please help with this simplification? Thanks.

anonymous · Answer

Is this at all related to your previous question? If not, would you mind posting the complete version of this one?

seascorpion1 · Answer

Original question 19a and my workings so far are now attached. I don't know where to go from here. Thanks in advance for your help.

seascorpion1 · Answer

@SithsAndGiggles

anonymous · Answer

Could you also post Equation (9)?

seascorpion1 · Answer

Equation 55 is the same as equation 9. Sorry if that wasn't clear.

seascorpion1 · Answer

@SithsAndGiggles Thanks' for your time, I've finally managed to solve this question. I'll post the solution later if I get a chance.