ODE45 to solve non-time function

I would like to use ode45 to solve the following D.E.

T'' + (1/x)*T' + G = 0

T'(x=0) = 0
k*T'(x=.5) + h*(T(x=.5) - 300) = 0;

where T = T(x) and G is a constant. I was told ODE45 can only be used for non-time equations but that can't be right because mathematically it doesn't matter. So I made the following substitution

f = T', f' = T''

then I get my system as

f' + (1/x)*f + G = 0
f(x=0) = 0
k*f(x=.5) + h*(T(x=.5) - 300) = 0;

But see I don't know how to deal with the T in the second boundary condition. Any advice?

[David Winthrop]

Perhaps the evening crowd will have some advice here? G is a constant.