Question

3. Use the method of variation of parameters to find a particular solution to the equation below. Then use your particular solution to find a general solution to the equation (give an explicit final answer in the form "y = ..."). y" - 9y = 14e3t

Answer 1

3 sol y"-94 = 14e34 homogeneous differential equation y"-94 = 0 on y" =D²y , y's Dy are te Day -99=0 (0²9)y=0 Acoscilary equation D²_q=0 (D+3)(D-3)=0 نوین در بدن دارد D =-3,3 it the roots are real and distinct diß the complementary solution is tyd by=+Get+62 eft Q=-3; B = 3 y(t) = C, est +2 est +C2 Ye(t) = 234 est particular solulim cyp): find the particular solution using variation parameter method is the right side function git). and complementary solution is Gelt) = gyit) + C2 y2ct) pparticula? solution is Ypresa A 4,(t) +BY ft)

- dt , B = WCE) در مورد از 12 دس درار در بازار git) Dani o y = e3t 1₂ et 3t 2 SU y=-3231 Slij with great Jistor 16. Diri A = -4/t)g() Яztate) wrt) pitosilmo prizrenas sport? y, it). 42Ft) where wit) #3 wronskics 276 Didget ini bermain di FP yist It) rögzite) 100 SA ye(t) = ciest + czeßt =agt (2 Y2 Hitt if (Djy puden grt) :14ě malaya y = 3 e3t 232,10 soit predlog xodlo C D at Bogu atstarop garni nom et et last 3 tony 3é3+34 e3+(-3e3+) = 3+3=6 3e3 land ann ha w(t) = 6 J Y2 g(6) A = dt. 9° Ju Santo on piticu luyland do not ac miradiva sti coopy bol A=-11 ens st 98429991 31 queens 18 depos : q? mikrobber so satan yirt)git) ē3+ (14e3t) B = edt 14 lidt= 7t wit) et 9 brewit) 3231 ermitico e3ti4e3t) 6t e dt داد) 6t 215 7 est 6

particular solution is. yolt) = A Yi + B yet ) ningizda de 1933 19 Brit Bitstaan doen 7 Bir Yol) (test).re36) +Chcet) 2 2017, dastle of Jot); - et+ 7te3ta storika)- (29922 darbo moiteista Yrit) = (t ets ($et Dond bitrio De Exibles) qorx? @22990 YT yplt) = 7 (6-1) 23t2 indem inn i en pod ) amoni 25 nainen type = 3:00 Boost particulas solution is! 18 7 ypt) = 09:25 for 1891 189 (6t-1) e3t General Solutions is y(t) = Yclt) + 4plt) Envienmis 83t+ (2. e3t +7 (6t-1e3t alpina 2 darin gitar sie -3t YOU) = ge 3E et + ² (6t-1) e ta 18