Closed form solution of differential equation

[equation M]

i have got a solution of my differential equation - consists of Bessel function and hyper-geometric function....should i call it as a closed form solution?

and i would also like to know about the importance of closed form analytical solution of any problem...what is the greatness of analytical solution over numerical solution?

thank you.....

 

[A. Bahat]

Whether you consider it closed-form or not is really just semantics. Sometimes closed-form just means "not expressed as a power series" (in which case you would have a closed-form solution to your equation); other times it refers to "elementary functions" (in which case you would not).