816 
MR. J. W. L. GLAISHER ON RICCATI’S 
so that the introduction of the constant a does not increase the generality of the 
solution. 
Returning to the integral (46), we find, on putting a = 0 and transforming the 
integral by the substitution t—i'v, 
u— 
{f — a?Y(e xv +e~ OT ) dv . 
w )dv 
= CxP +1 
Now, as will be shown in the next article, 
x ' 7 \x dx x 
so that the particular integral (49) is equivalent to 
The complete solution of the differential equation is, by art. 29, 
u— xp +1 
+V"). 
(48) 
(49). 
(50), 
which may therefore be written 
This is the complete solution in the form corresponding to (48). 
41. To prove the relation (50), let 
