DIFFERENTIAL EQUATIONS 181 



Special cases. 

 8.502 b z = bi = b = o. 



The solution is: 



yi = c^ ix + c 2 e^ x , 

 where: 



X2 202 



8.503 D - o, b 2 = o, 



where: 



c 2 Ce-( k+ ^ 

 J . 



k = m = X = 



^2 2#2 01 



8.504 D = o, 6 2 ^ o: 



where 



r w l 



^ = - W = 



2 



and X is the common root of: 



02\ 2 + fliA + OQ = O, 

 ^X 2 + bi\ + ^ = 0. 



8.505 D 4 1 o, b 2 = bi = o. If 77 =/() is the complete solution of 



where 



>, 



= X= 



402 



quation 8.500 

 be reduced to the form: 



402 02 202 



8.510 The differential equation 8.500 under the condition D ^ o can always 



8.511 Denote the complete solution of 8.510: 



8.512 b 2 = bi =-o: 



y = 



where: 



. fli gj 2 - 4^002 



~" : 



