Question

please states whaere the answer is .

(1 point) Solve y" + 2y + 2y = 4te-cos(t). 1) Solve the homogeneous part: y" + 2y + 2y = 0 for yo, using a real basis. Note the coded answer is ordered. If your basis is correct and your answer is not accepted, try again with the other ordering. Yn = 0^-t)cos( + e^(-t)sin((3 - 2) Compute the particular solution y, via complexifying the differential equation: Note that the forcing e cos(t) = Reſel-I+)). You will solve the complexified differential equation y" + 2y + 2y = 4tel-1+0) and The natural frequencies are: (Note: the answers are ordered. Try a different order if your answers are not accepted.) The forcing frequency is (use A, B etc. as your undetermined constants. The coding is Yp = ordered.) To solve for the undetermined constant(s), impose the criteria that y, solves the complexified non-homogeneous differential equation: y + 2y + 2y, = expo R+ 1+ . Note above: you collect like terms in 1. The coefficients are in general complex. So, A = Plug that back into y, and extract the real part for the original differential equation we set out to solve: Relyn) = Your full solution is y = yn + Rely).

Answer 1

y"+24'+2y= até t cost ausiliary equna m +2m +2=0 ma - 2 + 14-8 = -1 i se è t (el cost + Casint ) 2 t cost yo - 4t e - 20+02 2078244 -pe 4 : 0+20+2 29. manat el-1+i)t tilt = re. A D-iti +210-1+i) +2 - 1+0 = re Aetiti 0 - 20 ( - ) + ( - )” + 2) +2: * - Re All-ist +21D + 1-21-1720 t = Re a ellilt ortain t - Re qellise ocit est

SS 21 "Re 2 ell-it = Re 40-i) citest = Re qelli-i) zio (in ---) Tib (t-a) - Reļ 20-128, le ) - Re leccosa - isima) i : Re zet (ricost- sima) 1 + zet ( tcost esint , a tetceost -tsimt) ... 2 tsint) y = ét (Cicost it la sint ) + tetc cost