The following nonlinear differential equation was solved in Examples 24.4 and 24.7. 0 = d2T dx2 + h (T T ) + (T 4 T 4) (P24.5) Such equations are sometimes linearized to obtain an approximate solution. This is done by employing a first-order Taylor series expansion to linearize the quartic term in the equation as T 4 = T 4 + 4 T 3(T T) where T is a base temperature about which the term is linearized. Substitute this relationship into Eq. (P24.5), and then solve the resulting linear equation with the finitedifference approach. Employ T = 300,x = 1 m, and the parameters from Example 24.4 to obtain your solution. Plot your results along with those obtained for the nonlinear versions in Examples 24.4 and 24.7.

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