Find the general solution of this ODE \[
x^{2}\frac{d^{2}y}{dx^{2}}-x\frac{dy}{dx}+y=x
\]
To find
\[
\sum_{k=2}^{\infty}\dfrac{1}{k^{2}-1}
\]
We use this identity given from partial fractions $\dfrac{1}{k^{2}-1}\equiv\dfrac{\frac{1}{2}}{k-1}-\dfrac{\frac{1}{2}}{k+1}$
Then we use method of differences...try it
