366 Mr. B. Williamson on the Solution of 



°' (a'D.(*'D + l) + ^,)^=0: 



let x= —, then the transformed equation is 



.-. the solution is 



?/=Acos(fl^r4-a)=Acosf- +«j. . (5) 



(^D.(*D-l) + ^,)y=0. 

 The transformed equation is 



The solution of this is immediately seen to be 



y=As~^ cos {as + a). 

 Consequently the solution of the proposed is 



y = Awcosl- +ci) (6) 



This equation, when transformed, becomes 



accordingly the solution of the proposed equation is, by (3), 



y=A.--(^a-)"cos(| + «). . . (7) 



Ex. 4. Again, let 



(B,,?fe±l)B.$).=0. 



This is immediately transformed into the equation already dis- 

 cussed in (1) ; accordingly it has for its solution 



