how solve this differential equation?

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ghasem_008

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Hi
how solve this differential equation?
x²y'' + xy' = 1/(1-x) 0<x<1 ; y(0.5)=3

my problem is in inhomogenous part.

I know that it's homogeneous solution is :
y = - Ln(x)

how get its' inhomogeneous solution?
thanks
 

I think you should apply D'Alambert method to find a linear independent solution (from that you already found) of the homogeneous.
Then when you'll have y1h=-ln(x) and y2h=found using D'Alambert you can apply the Lagrange method to find the complete solution.
 


thank you very much fro your attentions...
So,I can not obtain a analytically solution?
 

thank you for reply
how use from advance Laplace transform in this problem?can you explain it,briefly?
 

how can I solve this equation by your suggestion?

- - - Updated - - -

how can I solve this equation by your suggestion?
 

Sorry, It's have copyright but if you try from basic,it's may be advanced. Try computer programming generate solution. The number of control point may in form 2N , I'm think should try sample by niquist rate .
 
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