like in example:1
I dont know how to find its exact solution.
Can someone provide its step wise solution? I really need help.
Find attached some of the papers related to HPM, additionally read some books related to this method. Unfortunately i can't recall any good book related to this method, hope some experienced researchers help you in this regard.Even then you still may not be able to find whole step by step tutorial so you have to solve or derive some equations by yourself.
The method of this article is restricted to simple methods and approximates only some terms of the solution. Analytical solution of Integral Equations is complex in general. If you are wiling, send me your problem, I can help you to solve it numerically.
Chapter 13 of Davis' "Introduction to Nonlinear Differential and Integral Equations" is devoted to this type of problem and may be of some help to you. This is a Dover book and can be purchased cheaply online, if you do not have a copy, for example:
http://www.amazon.com/Introduction-Nonlinear-Differential-Equations-Mathematics/dp/0486609715
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