Assume that the movement of barbaloots (or some animal) along the corridor is governed by a diffusion like process:

Q = -AD * dp/dx

Where Q is the diffusive flux of barbaloots (with units of number of barbaloots per day), p is the density of barbaloots in the corridor (number/m³), A is the cross-sectional area of a 1-m high slice of the corridor, and D is the diffusivity, with units of m²/day. Assume further that within the corridor, the barbaloots reproduce exponentially with a reproduction factor r, where r has units of day^-1 .

[a] After some time, the migration process reaches a steady state, whereby the density of barbaloots along the corridor does not change with time, though it does change with x. Starting with an equation for the mass balance of barbaloots, derive the 2nd-order differential equation governing the movement of barbaloots along the corridor.

[b] Invent some boundary conditions that would allow you to solve the problem, and state them clearly.

[c] Solve the problem.