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Mathematics. — On “Special cases of Monamr's Differential 
Equation” by Prof. W. Kapreyy. 
When the differential equation of Monae consists of three terms 
and has the form 
stiAt+u=—o0 
we formerly found all the cases in which this equation has two 
intermediate integrals. A further investigation of the equation 
r—Mttu—oO 
gives the following results. 
I. When A and « are dependent only on p and g, this equation 
possesses two intermediate integrals only when 
ig Ge ee 
— f+29qthg? Q 
and 
w= Ki(hQ—cP). 
Here K represents an arbitrary constant, whilst the six constants 
a, b, c, f, g, h are bound only by the condition 
acg — fh. 
If we put 5? —ac=a?, the two intermediate integrals are the 
following 
gt 2a 24h K[(g—b)r—cz]} ( 2a K(he+cy)), 
w (w—1) e ef NING ) 
where 
bd-ep—a gthq-—a 
WS ee 
behept gp hg pe 
and where f represents an arbitrary function 
—gq—# 2a —2e#hK[(gtb)x+0e 2] ( 2a K(ha—cy) ; 
wl) e A ) 
