Question

4 Find the general solution for y" – 3y' +2y = 1+e-?

Detailed answer, showing the integration

Answer 1

y"- 3yltzy. Het (1?-35+2)y= 14 Het of the form f1D).J= O(t) where fib) = 1²3p+2. Out) Auxilary equation as {(m)=0 m?_gmt2=0 -2m-m+2=0, mm-2)-1(M^2)=0 (m-1)(m-2)=0 m=12. complementary Function ycz ciet tege2 = cry, tc2Y2 Particulas solution's Jo= Alt) et +B(+)ezt. (: By method of variation of parameters). where Ya BC) = w (442) W(4,42) w(4192) = wlet ezt) dt at. et 2e2+ 3t Aft). .4 (ltet) et BCH) Jesu (ltet), et dt letti -dt 48² dt. Het

.t -4 Het Put q=et dq=-etde put Patet dp =-etat. 497 dq +q -- ef de - 4 Jeg et th) in na da 4 loge q+)--) da 1+q 4 log (itet). -- [ ] 1 -binada] -4q+H log(ite) 5-Hēt + 4 log (itet). "Particular solution ce Jp = log (itet).et+ (H tog intet)-hetheat 4 10g (htet) oct + 4 log (1+ēt)e+_ Het Geveral solutionica y = yc typ ya geticeet + hlog (itet), et + 4 log (itet), et the?