In[]:=
Clear["Global`*"];​​Eq=2*D[R[z],z]*D[u[z],z]+R[z]*D[D[u[z],z],z]==0;​​u[z_]=FullSimplify[​​DSolve[{Eq,R[z]^2*u[z]==R0^2*U0},{u[z],R[z]},z]]
Cloud
::timelimit
:This computation has exceeded the time limit for your plan.
​
Out[]=
$Aborted