Soluti 



Ordinary Linear Differential Equations of 2nd Order. 615 

 where 



lc + lif—k — b 1 ,73- ■ „ bc + li 7 bli — cci 



a = '~fr 2' r:= V^ 4 -^ /=-^2-? /= ->2"' 



(4) <" + g + *), + , { 2=J£* + «^ + (C W) } =0. 



olution : 



«=*»-» exp. { - ( C + ^}U P (|; - \ ; 2rx). 



(5 ) ^p.^Wjgzi^', ^^ eW| =Q> 



\# #*/ t A' 2 ^ A' 3 ^ #* J 



Solution : 



(6) t" + 2cxH' + t{(2c + q)x + (c 2 ~r 2 )^} = 0. 



Solution : 



, i - f , , r ^ 3 l TT /? 1 2r^\ 

 , =pe xp.{-(, + r)3lU, 6 (I-- 2 ; T ) 



(7) (b + x)t"+ {c+2fx)t'-(g + hx)t=Q. 

 Solution : 



« = (6 + A .)»exp.{ -(/+r)(6 + .r)U B (| ; -.| ; 2r(6 + f) } >_ 

 :-l 



where w = &/— ^— ; r = ^/Z* 2 + /i ; q = bh + 2bf" — cf—g. 



(8) /" + (2?> + 2ce mz X + * (/+ # fiTOZ + /ie2wx ) = °- 

 Solution : 



t= ^ v l-b x - c ^e™\j p!m L q --\ ; ->A 

 r \ ??z / y ' \2r??i 2 m / 



where r = ^/c' i — h; p^z^/b 2 —/; and q=f/ — cm — 2bc. 



(9) logs.*''+=^'+J^:=(). 



Solution : 



*=(log*)*-»Ui_*(A+P-i ; log*). 



