Question

find the general solution to the differential equation y''-5y+6y=x+1 using power series solution near ordinary point x=0

Answer 1

There is a \[y'\] missing in the differential equation.
Apply \[y=\sum_{n=0}^{\infty }a _{n}x^{n}\]
Then,
\[y'=\sum_{n=1}^{\infty} na ^{n}x ^{n-1}\] and
\[y''= \sum_{2}^{\infty } n(n-1)a _{n}x ^{n-2}\]
Plug those values in the differential equation?