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$\newcommand{\dd}{\mathrm d}$The equation is $\frac{\dd^2T}{\dd x^2} = h''(T - Ta)^4$

where $T(0) = 10$°C, $T(15) = 250$°C, $Ta = 30$°C

$h'' = 5.3*10^-8$, the step size is $0.1$, and initial guess of $z(0)$ and $T(0)$ are $8$ and $10$.

I know that the equation can be resolved into $\frac{\dd T}{\dd x} = z$, $\frac{\dd z}{\dd x} = h''(T - Ta)^4$

We're supposed to solve it with iterations, but I'm not quite sure how to proceed with the problem. Are we supposed to use the RK4 Method to find $T(15)$ at each initial $z$-value, then run that through a root-finding method such as the Secant Method? Or is it some other way to solve a nonlinear shooting problem, because I can't seem to understand how to execute the shooting method if the equation is nonlinear.

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