Problem of the week

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