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Re: Solving Third Order differential equation using Mathematica.


The differential equation can be solved for a=0, and if you series expand the differential equation in powers of a about a=0, discarding 2nd and higher powers of a, then it is still possible to solve it. I haven't investigated any further.

Here's what I did:

    DSolve[{Normal@
         Series[1/30 f'''[x] - f[x] (2 a^3/(1 - x a)^3 + 1/(1 - x)^3) - 
           24 a/(1 - y) (1/(1 - x)^7 - a^5/(1 - a x)^7), {a, 0, 1}] == 0, 
       f[0] == 0, f''[0] == 0}, f[x], x] // Simplify

I haven't quoted the output because it is quite large.



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