Question

\[(x-1)y''+y'=0\]
\[y=\sum_{n=0}^{\infty} a_n x^n\]
\[y'=\sum_{n=1}^{\infty} a_n x^{n-1}\]
\[y''=\sum_{n=2}^{\infty} n(n-1)a_n x^{n-2}\]

Answer 1

\[xy''-y''+y'=0\]
\[x\sum_{n=2}^{\infty}n(n-1)a_nx^{n-2}-\sum_{n=2}^{\infty}n(n-1)a_nx^{n-2}+\sum_{n=1}^{\infty} a_n x^{n-1}=0\]