Consider a homogeneous slab of thickness $2$L$,$ placed in a vacuum. The slab is centered on the origin of the x$-$axis. You can assume that $1-$g diffusion is valid; use zero$-$flux boundary conditions at the slab extremities and neglect the extrapolated distance. There is no fissile material in the slab. A constant uniform volumetric source S is present in the entire slab.

$1.$ Is the slab critical, subcritical, supercritical? Justify

$2.$ Solve that problem using exponential functions for the homogeneous solution.

$3.$ Solve that problem using hyper trigonometric functions for the homogeneous solution.

$4.$ Verify that the answers from $2$ and $3$ are identical using the identity formulas that relation

exponential and hyper trigonometric functions.