Question

3. Solve differential equation by undetermined coefficient methods y" + 2y' + 2y = 5e6r

Answer 1

0-3 5 egu y"+Qy' +2y = Let solve Homogenous Part First che] J-0 22 This is Linear Y" +2yltay=of- Homogenous ODE with constant coffi. We can get solution of Types So, ac mn e y! memn Дс me mu Using There in We bet (metam to) emmo As emne to matam+2=0 > m = -it solution of @ will be a (40) ex (c, aspak to sink ) Where ca are Just constants

Now To Get Particular solution, we will Une Method of Jaden Undetermined coffin Non - Homogenous term is seon All Derivative of apore ae will be of Type -A con u constons "A We will Look Look for a Particular For some So, solution of Typeg on = A e y = 6 A Cox Yo =26 A eon Use There in There in Gu 625 con 36A e + 12 A e tae (36A +12A +2) cbx = 5 con 48 A +2 = 5 n --- А 48 16 so, Generdselution of 0 is criven burg Lot 4 = EC, csx + Gelin + 6R e