second order ode45-where to put boundary and initial condition?

I am solving this equation with ode45 method, p0 is already known:

4B*d^2u/dr^2+(4B/r)*du/dr=dp0/dz

and I have two conditions,

initial condition: r=0: du/dr=0;

boundary condition where r=1: u=0.

Where to put these conditions, because I can put initial condition in ode45 solver, but where to put boundary condition in this case?

Answer 1

[Torsten]

u(r) = -1/(16*B)*dp0/dz*(1-r^2)

If the analytical solution is not what you want, use "bvp4c" instead of "ode45".

Best wishes

Torsten.