For #11 in section 5.3:

The table in the back of the book is just wrong.  It should say:

i    t_i    y_i
1    0.250  0.75000
2    0.500  0.62500
3    0.750  0.57353
4    1.000  0.56360

Correctly used, the Java applet (http://www.csun.edu/~hcmth018/SysEu.html)
gets these correct numbers.

I checked them myself with this low-tech use of Matlab/Octave.
(Use the up-arrow key.  That is, I only entered interesting stuff once
and then hit up-arrow and return three more times.):


>> t = 0, y = 1,v = -1
t = 0
y =  1
v = -1
>> h = 0.25
h =  0.25000
>> ynew = y + h*(v); vnew = v + h*((y-v)/(1+t*t)); y = ynew, v=vnew, t = t + h
y =  0.75000
v = -0.50000
t =  0.25000
>> ynew = y + h*(v); vnew = v + h*((y-v)/(1+t*t)); y = ynew, v=vnew, t = t + h
y =  0.62500
v = -0.20588
t =  0.50000
>> ynew = y + h*(v); vnew = v + h*((y-v)/(1+t*t)); y = ynew, v=vnew, t = t + h
y =  0.57353
v = -0.039706
t =  0.75000
>> ynew = y + h*(v); vnew = v + h*((y-v)/(1+t*t)); y = ynew, v=vnew, t = t + h
y =  0.56360
v =  0.058412
t =  1