Example

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

Plot the slopefield for $x' \,=\, 2\,t\,x$ over the rectangle $1 \,\leq\, t \,\leq\, 4$, $-2 \,\leq\, x \,\leq\, 0$. Investigate whether this rectangle gives a good overall picture of the ODE behavior. If not, plot over a better 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. Type slopef(ftx,N) to obtain
   
   
   

Since $x' \,=\, 2\,t\,x$ represents the slope, we should also consider when $t < 0$ and $x > 0$. Suppose we try the symmetric rectangle $-2 \,\leq\, t \,\leq\, 2$, $-2 \,\leq\, x \,\leq\, 2$.

1. This time change only

   initax = [-2,2,-2,2];

   Save then type init in the command window (or copy-and-paste in the Emporium).
2. Type slopef(ftx,N) to obtain
   
   
   

Build your intuition: Does this picture match the general slope behavior indicated by $x' \,=\, 2\,t\,x$? Look at the following cases

$$\mbox{(a)}\;\; t < 0, \;\; x > 0, \qquad \mbox{(b)}\;\; t < 0... ...;\; t > 0, \;\; x < 0, \qquad \mbox{(d)}\;\; t > 0, \;\; x > 0$$