How to integrate $r^2\frac{d^2U(r)}{dr^2}+2r\frac{dU(r)}{dr}=0$?

Question

The function is given as

$r^2\frac{d^2U(r)}{dr^2}+2r\frac{dU(r)}{dr}=0$

I have to integrate this 2 times and apply

$U(r_0) = V$

$U(\infty)=0$

The answer should be

$E = \frac{V}{r_0}$

I am not getting the same answer? Can someone please check what I am doing wrong:

$\int_{r_0}^{\infty} (r^2\frac{d^2U(r)}{dr^2}+2r\frac{dU(r)}{dr})=0$ gives

$Vr_0^2+2r_0\frac{V^2}{r_0}=E$

but that doesnt give $E = \frac{V}{r_0}$