Ah, this is a nice heat transfer homework problem! The function you're looking for in MATLAB for coding up the solution is called ode45.
The help file documentation here should help you set up the equations you need: https://www.mathworks.com/help/matlab/ref/ode45.html. Pay close attention to the section entitled "Pass Extra Parameters to ODE function" to see how to handle the second order derivative. One of the "fun" revelations of calculus is that a function has a first-order derivative, and that derivative can be treated as a first-order function itself that has a derivative (which is the second-order derivative to the first).
Let us know if you have further issues writing the code and we can help you troubleshoot.
