Find the general solution of $y*{\prime \prime)- x^{2} y {\prime)-y=0$ by power series method \begin tabular}{111) Whline A) & $\mathrm{RF}$ (recurrence formula): $a_{n+2)=\frac{-1}(n+2) (n+1) a_{n-1}$ & $y=a_{0}\left(1-\frac{1}{6} x^{3}+\frac{1} (180) x^{6}+\cdots ight)+a_{1}\left(x-\frac{1}{12} x^{4}+\frac{1}{504) x^{7}+\cdots ight) \end{tabular] B) $$ \begin{array}1) \text { RF:) a_{n+2)=\frac{2}{(n+2)} a_{n} W y=a_{0}\left(1+x^{2}+\frac{1}{2}x^{4}+\frac{1}6) **{6}+\cdots ight)+a_{1}\left(x+\frac{2}{3} **{3}+\frac{4}{15} x {5}+\frac{8}{105) **{7}+\cdots ight) \end{array} $$ C) $$ \begin{array}{1} \mathrm{RF): \quad a_{n+2}=\frac{-1}(n+2)} a_{n-1} y=a_{0}\left(1-\frac{1}{3} x^{3}+\frac{1}18) x^{6}+\cdots ight)+a_{1}\left(x-\frac{1{4} **{4}+\frac{1}{28) **{7}+\cdots ight) \end{array} $$ D) $$ \begin{array}{1) \text {RF: 1 a_{n+2}=\frac{n-1} (n+2)(n+1)} a_{n- 1}+\frac{1}{(n+2)(n+1)} a_{n} \ y=a_{0}\left(1+\frac{1}{2} x^{2}+\frac{1}{24] x^{4}+\frac{1}{20] **{5}+\cdots ight)+a_{1}\left(x+\frac{1}{6) **{3}+\frac{1}12} x^{4}+\frac{1}{120) x^{5}+\cdots ight) \end{array} $$ SP.SD. 407