PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 283 
+ 
Ex. 4. +ax+by+e2=0 
aby ; 
a9 +a x+Uy+e72=0 
d} z 
ae % pa’utd'yte’z=0 
These equations can be written in the form 
Agv+by+ez=0 
adx+By+e2=0 
a’ a+b" y+O0"z=0 
_ By eliminating y and ¢ we obtain 
fA B C’—8'¢ A—a’ cB—a' 60" +a b' c+" bclw=0 
3 
or { a? +(a+0' ) d ee cl b ua d? b Ui 
18 +e qt @ ac’ + Se ae c 

de d* dé 
0 Ae a Oe 0 Ct 0 C= 0 Ol e. 
d t? d t} dt} 
+a'era’be } «2=0 
4 a tacl4¥ e—be'—a'e Ha 



dz 
or { ; 
d ¢ 
capital eiieeiar 
dt? 
which is of the same form as Cor. 2, Ex. 3, Class 1, and its integral is therefore 
known. 
oe az, we have by + cz=/(t) by the first of the three equations, 
by 
and ae oH 229 (¢) by differentiation, whence, by substituting the values of 
bs 
vt oo and © = = from the second and third equations, there results a second equation 
between y, z, and ¢. From these two equations y and z are determined in terms 
of t. 
, dz 
Ex. 5. Given Eee pg SID ic A 
These equations may be written 
(d+ad!+b)x=(pdtqdit+r)y 
(d+ dt+6)a=(pd+qddt+r)y 
