Help with differential equations regarding even/odd functions, IVT

[Jboulos12]

Here's the problem i need help on. It can be found in Nagle's Differential Equations 8th edition chapter 8.3 number 32.

http://hostingbytes.us/images/3/6025942.jpg

i first tried to solve this using the power series and got:
a2=a0
a(k+2) = 2ak/(k+2)

after this, i have no idea how to solve a-d. any help will be greatly appreciated. I have my test tomorrow so please be urgent!

 

[HallsofIvy]

You got more than that didn't you? What you give tells us only the coefficients with even index. What did you get for $a_k$ with k odd?