I just finished a final in my differential equations class. One of the problems had me solve a second order homogeneous differential equation using series. I boiled it down to this recursion relation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a_{n+2}=\frac{(n+3)a_{n}}{2(n+2)(n+1)}[/tex]

I found that the even coefficients work out nicely to the following sum:

[tex]y=a_{0}+\Sigma^{\infty}_{n=2}\frac{(n+1)a_{0}}{4*6^{n-2}}x^{n}[/tex]

I couldn't get a nice result for the odd coefficients and still can't find one. It's kind of bothering me now. Is it even possible? I can boil it down to this series:

[tex]\frac{1}{3},\frac{1}{20},\frac{1}{210},\frac{1}{3024},\frac{1}{55440},...[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A series

**Physics Forums | Science Articles, Homework Help, Discussion**