Solve 2nd Order ODE: Step by Step Guide

[justsmile92]

Please see the attached description of the problem I need to split the second-order o.d.e to two first-order o.d.e's.
(numerically)

Then use the shooting method with a 0.5 step size to solve the system of equations.
(This needs to be done on an excel spreadsheet)

Then to plot the temperature along the body.
(not sure how to do this)

I don't know where to start! Can anyone help!

 

[HallsofIvy]

Your second order ODE is
$$\frac{d^2T}{dx^2}+ a(x)\frac{dT}{dx}+ b(x)T= f(x)$$

Let S(x)= dT/dx and that becomes
$$\frac{dS}{dt}+ a(x)S+ b(x)T= f(x)$$
so your two first order equations are
$$\frac{dS}{dx}= -a(x)S- b(x)T+ f(x)$$
$$\frac{dT}{dx}= S$$