init.m

This is the file you will use/modify for submission of each first order ODE/IVP ² to MATLAB. Its corresponding MATLAB command is init (the filename minus the .m extension). Each time you change the ODE ftx, the symbolic solution ftxsln, or any of the associated parameters/conditions, this file must be edited, saved, and init must be typed in the command window (or copy-and-paste at the Emporium). For a complete description of init.m, see `` init.m Line-by-Line'', §1.3, page . The lines you will be most concerned with are

$$\mbox{\tt ftx= \dots; \% Enter \dots}$$ (1)

$$\mbox{\tt initax=[$\cdots$]; \% Enter \dots}$$ (2)

$$\mbox{\tt t0= \dots; x0= \dots; \% Intital conditions \dots}$$ (3)

$$\mbox{\tt C= \dots; \% Initialize \dots}$$ (4)

$$\mbox{\tt ftxsln= \dots; \% Enter \dots}$$ (5)

(1) ftx is the RHS of the ODE $x'=f(t,x)$.
(2) contains the axis ranges for the graphics display. You will adjust these to find the best ranges to view your graphics.
(3) are initial conditions you will enter after obtaining them via slopef and sol1. Hence whatever values are there at the beginning of a problem are generally immaterial. However you must have specific numerical values entered there.
(4) is obtained by hand from substituting t0, x0 into your symbolic solution ftxsln.
(5) is the symbolic solution $x = \dots$ to the ODE $x'=f(t,x)$. You will obtain this by hand via the various techniques we will study.

Two things are important to repeat: DO NOT remove any lines from init.m, and be sure to use single quotes with the RHS expressions for ftx and ftxsln.