This is the same as above problem where we found\[ y_{h}=a_{0}\] To find \(y_{p}\) we will use the balance equation (*) from the above problem which is\[ rc_{0}x^{r-1}=x^{-2}\] Hence \(r-1=-2\) or \(r=-1\). Therefore \(rc_{0}=1\) or \(c_{0}=-1\). The particular solution is therefore\[ y_{p}=-x^{-1}\] Hence the solution is \begin{align*} y & =y_{h}+y_{p}\\ & =c_{1}\left ( 1+O\left ( x^{2}\right ) \right ) -\frac {1}{x}\end{align*}