https://en.wikipedia.org/wiki/Adomian_decomposition_method

Thanks sir. My problem is how to generate the recursive terms i.e  how they gor yo, y1 ...

Please see the book of Abdul-Majid Wazwaz

Partial Differential Equations and Solitary Waves Theory.

The highest order of the ODE is replaced by L, say L=dny/dtn .

Rearrange the equation as LHS=y and RHS contains the term L-1

Once you substitute the assumed solution y = y0+y1+y2+... in the equation, you can compare the terms on LHS and RHS to get y0,y1, etc.

y0 will be given by the terms on RHS which doesn't have any of y0,y1,y2,etc.

y1 will be given by the terms on RHS which contains y0

y2 will be given by the terms on RHS which contains y1...

yi will be given by the terms on RHS which contains yi-1...

thanks it helps a lot

DOWNLOAD JOURNAL ARTICLES BY WAZWAZ AND RACH,

See the attached files. You can do it by these papers.