Œuvres de Charles Hermite publiées sous les auspices de l'Académie des sciences, par Émile Picard.

i,26

OEUVRES DE CIARLES HERMITE.

If then
T=(i)( t3- 3t2- t --
we have
t(t -+ ) t 44 ( t- ) t
_4- t + fi) T
whence
X du 5 dt
I T
whence
5 r t
a =_r clt
Consequently the question is integrable by elliptic functions
The other examples are contained in the type
3 — 3Pv2 -4 4Q = o
(with the condition Pi3 +- Q R2).
P, Q, R being integral functions of u of the degrees 2, 6, 3.
3But this equation may be writen
(v + 2 P)2)(v -P) =- (P3- Q) =-4RI,
and on writing
2Kt
v + -2 P = — -
becomes simply
(3 3 P w - 2R = o.
And this transformed equation being of the degree 3 in w,, u,
these two quantities, and consequently also c, u, can be expressed
as rational functions of t and of an elliptic radical.
The equation F (- it) gives rise to similar substitutions.
(dnu