24 
[637 
637. 
ON A DIFFERENTIAL EQUATION IN THE THEORY OF ELLIPTIC 
FUNCTIONS. 
[From the Messenger of Mathematics, vol. vi. (1877), p. 29.] 
In the differential equation 
<? - a (, + l)_ 3 = 3 ( 1 -P)§, 
considered Messenger, t. iv., pp. 69 and 110, [594] and [597], writing Q = x and 
k + ^ = y, the equation becomes 
, 3 (y 2 — 4) dx 
dy = a+ v -* ■ 
and we have, as a particular solution, 
To verify this, observe that from the value of y 
dy = ^ (x 2 — l) 2 dx, 3 + xy — x 2 = \(x 2 — 1) (x 2 — 9), 
and the equation becomes 
{(¿c 4 — 6x 2 — 3) 2 — 64a? 2 } 
viz. this is 
4ie 2 ^ ‘ J {a? — 1) (x 2 — 9) 
which is right. 
(x 2 — l) 3 (x 2 — 9) = (¿r 4 — Qx 2 — 3) 2 — 64^,