264 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
By substituting this in equation (2) we obtain 







gee shi */( nt 2 ill pope & 
dank Mm LV) &@ 7 Re td dan) + e.) =0 
ne d” z rE ae ib Pimae 1.1 a@—1) dz 
ax” 24 m?a2™)dam-1 2.4 242  gan-2 
1.1.3%(n—1) (n—2) qr-3 z n-11.1.3...2@n—3 
‘oy ding: eae ge cogs Ott SAL a ona 5, oem 
' n(n—1)...1_9 
qn 
When z has been determined from this equation, we shall have the complete 
value of y by means of Equation (1.), viz. 
Ya a o a —t2 
ae pss 

y= 
Cor. If Wes 
0. 

d «3 2a m2 ae6)/da?® Aatda 823 
d3 z (= ll i Heo oO 
which is the same equation as that which we obtained by a totally different pro- 
cess for determining y, and y, in Ex. 6. 



n d?y 
Bx. 3. —ma ——~= XK 
2 ° d a? 
The solution is 
1 Lima dt 
=— ——,(X+0) = x 
Y 1—m2” ag A +2) 1—m? x" d? a” dt Ce 
=(1+m" d?) (v+w) 
n au n aw 
—v+me +wtm az 
dat d xt 
where 7 is the same as in the last Example, and w is determined from the 
equation 
4 nm qt 
w—m x” 2 (5) —X 
d xt dat 
n—1 
or by writing — for w, and proceeding as in the last Example, 



=] a” n erat d?-ly 
oh se ee en ee Se Or 
da®—} d x” 2 ae 
