Use Euler's method to approximate a solution to the ODE . By hand, set up the iterating equation and solve for three iterations using the initial condition and step size . Next investigate both Euler's method and the 4th order Runge-Kutta method graphically usingnum3plotwith the four step sizes . Identify each plot with its respective step size. Explain the rather odd behavior for with when all plots are compared. You may need to calculate a few Euler iterations by hand for these step sizes. (Does this suggest more than one way that step size can affect results?)

- Iterating equation
with

- Change only the following in
`initn.m`ftx='2*t*x'; eulerfcn='x+h*(2*t*x)'; hvec=[.5,.25,.1,.01]; t0=-2; tf=2; x0=1;

Save, then type`initn`to initialize the variables (or copy-and-paste at the Emporium). - Type
`num3plot` - Here one should investigate and show results such as in Item 4,
pp , for
`eulplot`.

For , we have

Each subsequent iteration will also be zero.

For , we have

Each subsequent iteration will also be zero. - The finished product is on the next page. (Note: your work in
the upper left will be neatly hand written, not typed.) Also be sure
to identify which approximation goes with which stepsize from
`hvec`for all three graphs.