58] 
JACOBI S SYSTEM OF DIFFERENTIAL EQUATIONS. 
369 
dy 
viz. multiplying by the factor 2 —,, and integrating, 
, = c. 
y 
dt 
Hence replacing y and ^ by their values 
we have 
an d -¡«ï^ y 
Fa k - LFa = G, 
{ (a - x) F x) Fa 
for one of the integrals of the proposed system of equations : and since a is arbitrary, 
the complete system is obtained by giving any (n— 1) particular values to a, and 
changing the value of the constant of integration C ; or by expanding the first side 
of the equation in terms of a, and equating the different coefficients to arbitrary 
constants. The à posteriori demonstration that all the results so obtained are equivalent 
to (n — 1) independent equations would probably be of considerable interest. 
c. 
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