Differential equations like the one solved in Prob. 27.6 can often be simplified by linearizing their nonlinear terms. For example, a first-order Taylor series expansion can be used to linearize the quartic term in Eq. (P27.6) as

1 x 10^-7 (T + 273)⁴ = 1 x 10^-7 (T_b + 273)⁴ + 4

x 10^-7 (T_b + 273)³ (T - T_b)

Where T_b is a base temperature about which the term is linearized. Substitute this relationship into Eq. (P27.6), and then solve the resulting linear equation with the finite-difference approach. Employ T_b= l50 and ∆x = 0.0l to obtain your solution.