Help with differential equations regarding even/odd functions, IVT

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SUMMARY

The discussion focuses on solving a differential equation from Nagle's Differential Equations 8th edition, specifically from chapter 8.3, problem number 32. The user initially applied power series methods, resulting in the coefficients a2 = a0 and a(k+2) = 2ak/(k+2). However, they encountered difficulties in determining the coefficients for odd indices (a_k with k odd) and sought urgent assistance before an upcoming test.

PREREQUISITES
  • Understanding of power series methods in differential equations
  • Familiarity with Nagle's Differential Equations 8th edition
  • Knowledge of even and odd functions in mathematical analysis
  • Basic skills in solving differential equations
NEXT STEPS
  • Review the section on power series solutions in Nagle's Differential Equations 8th edition
  • Study the properties of even and odd functions in relation to differential equations
  • Learn how to derive coefficients for power series expansions
  • Practice solving similar differential equations to reinforce understanding
USEFUL FOR

Students preparing for exams in differential equations, educators teaching mathematical analysis, and anyone seeking to deepen their understanding of power series methods and their applications in solving differential equations.

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!
 
Physics news on Phys.org
You got more than that didn't you? What you give tells us only the coefficients with even index. What did you get for [itex]a_k[/itex] with k odd?
 

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