Solve the problem of heat generation in a slab with a variable thermal conductivity. Show that the problem can be represented as

\[\frac{d \theta}{d \xi}\left[(1+\beta \theta) \frac{d \theta}{d \xi}\right]=-1\]

with the boundary condition of no flux at the center and convective heat loss at the surface, where \(\beta\) is the coefficient in the thermal conductivity relation. Thus \(\beta\) equal to zero is the base case of constant conductivity.

Obtain a regular perturbation solution with \(\beta\) as the expansion parameter.