A boundary value problem

by scott   Last Updated August 14, 2019 06:20 AM

I am trying to solve the following boundary value problem:

$$ x^2 u'' + 2 x u' - 2u = 18x^4,\;\; 0 < x < 2, \\ u \text{ finite},\;\; x \rightarrow 0^+, \\ u' - u = 0, \;\; x = 2. $$

I'm not sure how to go about this. So far I've solved it for the homogeneous case and got $v = Ax^{-2} + Bx$ and not sure where to go from here. The answer in my texbook is $u = 16x + x^2$. Any help is appreciated.



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