LINEAR EQUATIONS. 
205 
Given two algebraic equations involving the same unknown 
quantity and of the respective degrees m and n, we can 
deduce by their combination a new equation of the degree 
m~n. 
Given two linear equations involving the same variables 
and of the respective orders m and n, we can deduce by 
their combination a new linear equation involving the same 
variables and of the order m ~ n. 
Many other properties exemplifying the general analogy 
might be noted. Fuller demonstration of those above noted 
will be found in Moigno, Calcul Intégral, Tom. 11. p. 579. 
EXERCISES. 
- 4 ^+3' = 0- 
d 3 y d\ 
lb? ~ ^ Thcr + ty — ^ being given that one of the 
5. 
roots of the auxiliary equation, m 3 — 3m 2 + 4 — 0, is 1. 
8. What form does the solution of the above equation 
assume when & = 1 ?