Originally Posted by
DeMath Multiply by $\displaystyle r$
$\displaystyle u'' + \frac{u'}{r} = 0 \Leftrightarrow ru'' + u' = 0 \Leftrightarrow \left(ru'\right)^\prime = 0 \Rightarrow ru' = C_1 \Leftrightarrow u' = \frac{C_1}
{r} \Rightarrow u = C_1\ln|r| + C_2.$