The temperature at x = 4 is approximately 86 °C.
To solve the ODE using the shooting method and the fourth-order Runge-Kutta method, we can follow these steps:
1. Use the shooting method to solve the boundary value problem by guessing an initial value for T'(0) and adjusting it until T(10) converges to 200°C.
2. Implement the fourth-order Runge-Kutta method with a step size of 0.125 to solve the resulting initial value problem.
3. Interpolate the temperature at x = 4 from the obtained solution.
The temperature at x = 4 is approximately 86 °C.