What if we let PSKu(t)=1/r(t)? Then

\(\displaystyle{r}'=-{\frac{{{1}}}{{{u}^{{2}}}}}{u}'\) and \(\displaystyle{r}{''}={\frac{{{2}}}{{{u}^{{3}}}}}{\left({u}'\right)}^{{2}}-{\frac{{{1}}}{{{u}^{{2}}}}}{u}{''}\)

Hence

\(\displaystyle{r}+{\frac{{{2}}}{{{r}}}}{\left({r}'\right)}^{{2}}-{r}{''}={\frac{{{1}}}{{{u}}}}+{2}{u}{\left(-{\frac{{{1}}}{{{u}^{{2}}}}}{u}'\right)}^{{2}}-{\frac{{{2}}}{{{u}^{{3}}}}}{\left({u}'\right)}^{{2}}+{\frac{{{1}}}{{{u}^{{2}}}}}{u}{''}\)

\(\displaystyle={\frac{{{u}+{u}{''}}}{{{u}^{{2}}}}}\)

Can you take it from here?

\(\displaystyle{r}'=-{\frac{{{1}}}{{{u}^{{2}}}}}{u}'\) and \(\displaystyle{r}{''}={\frac{{{2}}}{{{u}^{{3}}}}}{\left({u}'\right)}^{{2}}-{\frac{{{1}}}{{{u}^{{2}}}}}{u}{''}\)

Hence

\(\displaystyle{r}+{\frac{{{2}}}{{{r}}}}{\left({r}'\right)}^{{2}}-{r}{''}={\frac{{{1}}}{{{u}}}}+{2}{u}{\left(-{\frac{{{1}}}{{{u}^{{2}}}}}{u}'\right)}^{{2}}-{\frac{{{2}}}{{{u}^{{3}}}}}{\left({u}'\right)}^{{2}}+{\frac{{{1}}}{{{u}^{{2}}}}}{u}{''}\)

\(\displaystyle={\frac{{{u}+{u}{''}}}{{{u}^{{2}}}}}\)

Can you take it from here?