Example 1

When you first copy init.m, it should be set to run this example.

Plot a slopefield for $x' \,=\, 2\,t\,x$ over a rectangle illustrating the general characterisics of the ODE. Then plot one solution to the ODE within this rectangle.

1. Change only the following in init.m

   ftx = '2*t*x'; (``$*$'' indicates multiplication)
   initax = [1,4,-2,0];

   Save then type init in the command window to initialize the variables (or copy-and-paste in the Emporium).

2. See the example for slopef, page , to investigate the window size initax = [1,4,-2,0]; then make the change to initax = [-2,2,-2,2]; in init.m. Save then type init in the command window to initialize the variables (or copy-and-paste in the Emporium).

3. Type sol1. Answer ``y'' to draw new slopefield
   
   
   

4. Have MATLAB draw a solution close to $(t_0, x_0) \,=\, (1,1)$ by clicking near that initial condition on the slopefield.
   
   
   
   From the graphics display we observe the actual $(t_0, x_0)$-value. (In this case $(1.0932, 0.95208)$.)