You can use WolframAlpha to solve this

http://www.wolframalpha.com/input/?i=y%27%27%28x%29-%28a^2%29*y%28x%29%3Darcsin%28x%2Fb%29

Then you get two integrals to evaluate which you can use WolframAlpha again to get a series solution. See attached files

Dear Prof ,

      You  can try to use some mathematical softwares like  Mathematica .

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Best Regards ,

Dr/Tarek Ibrahim ( T. F. Ibrahim )

Associate professor

¹Current address : Department of Mathematics, Faculty of Sciences and arts (S. A.) ,King Khalid University, Abha , Saudi Arabia

²Permanent address: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.

E-mails: [email protected]

[email protected]

[email protected]

Personal Websites :

http://eupc.mans.edu.eg/V2/get?Dr=27311031200455&T=2&L=A/

http://eupc.mans.edu.eg/V2/get?Dr=27311031200455&T=2&L=E

https://www.researchgate.net/profile/Tarek_Ibrahim2/?ev=hdr_xprf

http://scholar.google.com/citations?hl=en&user=K0uEihsAAAAJ&sortby=pubdate&view_op=list_works&pagesize=100

Dear Prof,

Please find in attachment the answer on yours question.

Sincerely,