Help with differential equations regarding even/odd functions, IVT

Jboulos12
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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!
 
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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?
 

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