826 
MR. J. W. L. GLAISHER ON RICCATI’S 
r being put equal to cd after tbe differentiations, and 
u=Cx p+l \ (r 3 — a?) 1 * cos (rx-\- a)dr. 
•J —a 
See arts. 37, 39. 
(xi.) 1839. Hymers. ‘A Treatise on Differential Equations and on tbe Calculus 
of Finite Differences’ (1839), pp. 83-85 ; also, second edition (1858), p. 125. 
Solution of Mr. Gaskin’s problem in (x.). See art. 37. 
(xii.) 1841. Ellis. “On tbe Integration of Certain Differential Equations,” 
‘Cambridge Mathematical Journal,’ vol. ii., pp. 193-195. 
Independent investigation of tbe first of Mr. Gaskin’s forms in (x.). See art. 37. 
(xiii.) 1841. De Morgan. ‘Tbe Differential and Integral Calculus,’ pp. 702-704. 
Account of Ellis’s method (see xii.) and of Poisson’s determination of tbe integrable 
cases of Riccati’s equation (see viii.). See arts. 36, 37. 
(xiv.) 1844. Boole. “ On a General Method in Analysis,” ‘Philosophical Trans¬ 
actions’ for 1844, pp. 251, 252. 
This paper contains Boole’s general symbolic method. The solution of the equation 
(1) is given in tbe form 
c x e ax + c 2 e 
x 
2i—1 
The general method and this solution are reproduced with only slight changes in 
Boole’s ‘Differential Equations,’ chapter xvii. See art. 34. 
' . Ill 
(xv.) 1846. Lebesgue. “ Remarques sur l’Equation y"-\~ -y'-{-ny—0,’ ‘ Liouvilles 
Journal,’ vol. xi., pp. 338, 339. 
Solution of this equation in a form involving repeated differentiations with regard 
to x. See art. 37. 
(xvi.) 1848. Hargreave. “On the Solution of Linear Differential Equations,” 
‘Philosophical Transactions’ for 1848, pp. 34, 35, 45. 
The paper contains the general integral of (1) in the forms, 
u 
u 
p pax i r r —ax 
■= P +1 (D 3 — a?) 1 A- 6 ®—, 
= c 1 .r _ j' , J (z 3 — lyp-^e^dz+c^xP^ (z 3 —1 )Pe ax "dz, 
C a ' x 
and a development of (D 3 — a~) 1 — in a series. There are also solutions of other allied 
equations. See arts. 41, 42. 
