CHAPTER XXI 

 176. If y - A sin nx 4- B cos nx, 



-4- = wA cos nx riB sin nx 

 dx 



-^- = - n 2 A sin nx - n 2 B cos nx 

 dx 2 



= n 2 (A sin nx + B cos nx} 

 = -n 2 i/ 

 Thus the solution of the differential equation -~ 4- n 2 */ = can 



be assumed to be y = A sin nx + B cos nx where A and B are 

 constants. 



If y = Ae"* + Ee-"*, 



dx = 



dx 2 ^ 



- n 2 (Ae na! + Be-"*) 



d 2 ?/ 

 Thus the solution of the differential equation -r-^ - ri*y = can 



be assumed to be y = Ae"* + Be-"* where A and B are constants. 



dhi 

 Also for the differential equation ^ = ri*y a general solution 



y = kf* can be assumed, k being a constant. 

 For if y = 



Hence y = A^ 8 " is a solution of the equation ^ = rihj if <x a - n* 



or a = n, 



and t/ = Ac 1 *" 4- Bc"'"* is the complete solution 



349 



