Hence 
USGS) S08) = CE a) a7 (Ce) 
= Ol GE) se) Crement=)) mya Ct) 
or if y # 0, 
TL =O (5p) eOlGee se) (1.14) 
Differentiating with respect to t yields 
o® 
Cie es 
(t, 7) @(t, t) + O(t, 1) Z O(t, t) 
A(t, 1) O(t, t) + O(t, 1) $ act, ¢) 
A(t) + (t, 1) £ (2, ¢) 
It can be shown that 9(t, Tt) has an inverse and that this inverse is 
O(t, t); consequently 
4 OG, Boo OE wD Ate) = = OG, &) AG) 
that is, ®(t, T) as a function of T satisfies 
oC, T) = - O(t, T) A(t) (1.15) 
Although (1.15) will be used subsequently, of immediate interest is the 
solution to the inhomogeneous linear equation 
y = Ay te (ee) (1.16) 
10 
