Boundary Value Problems $($BVPs$)$ may be solved using standard initial$-$value$-$problem integrators $($like ode$45)$ by guessing the some of the initial values and checking to see if those produce the required final values $($as with the in$-$class temperature problem$).$ Here, use an automated technique $($specifically$,$ root finding$)$ to determine the temperature distribution in a circular rod with internal heat source S$,$ governed by the differential equation: