Question

equations difference help

Answer 1

working with \[3xy''+y'-y\]

Answer 2

guess \[y' = \sum_{n=0}^{\infty} (n+r)c_nx^{n+r-1}\] and \[\sum_{n=0}^{\infty}(n+r)(n+r-1)c_nx^{n+r-2}\]

Answer 3

so \[3xy'' + y'-y=3\sum_{n=0}^{\infty}(n+r)(n+r-1)c_nx^{n+r-1}+\sum_{n=0}^{\infty}(n+r)c_nx^{n+r-1}-\sum_{n=0}^{\infty}c_nx^{n+r}\]

Answer 4

i stuck here.