Solution
= Solution
Multiplying $Dn\prime\prime+f(n)=0$ by $n\prime$ and using the endpoint conditions gives the logistic front
$$
n_0(x)={1\over1+e^{x/\sqrt{2D}}}.
$$
It has $n_0(0)=1/2$ and direct differentiation verifies the equation for $r=1/2$.