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## Homework Statement

this is Cauchy's LDE.. someone help me to solve this equation.

x^2 y'' + 3x y' + y = 1/(1-x)^2

## Homework Equations

## The Attempt at a Solution

i started it with substituting

x= e^t

then ln x = t

and d/dt = D

hence the equation becomes

{ D(D-1) +3D +1} y = 1/(1+e^t)^2

and i got characteristics equation

as

Yc=(c1 + c2x ) e^-1

now i have problem in findind Particular Intergral i-e Yp..

i-e

Yp = 1 / {(D+1)^2 (1+e^t)^2 } ???

somebody help to complete its solution?

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