$P20\mathrm{.}2$ Show that the function $(\frac{r}{a_0})e^{-\frac{r}{2}{a}_0}is$ a solution $of$

the following differential equation for $l=1$

$-\frac{{}^2}{2m_e{r}^2}\frac{d}{dr}[r^2\frac{dR(r)}{dr}]$

$+[\frac{{}^{2}l(l+1)}{2m_e{r}^2}-\frac{e^2}{4{}_{0}r}]R(r)=ER(r)$