Question

(4)Use variation of parameters to find the general solution of da 3r-3y+4 dt dy = 2x- 2y-1 dt

Answer 1

dr 3-39+4 dt dy 2 2y-1 dt % -3 (2 :) + dn 6 Ax+ 9 Consider Homosenous S1stem F 9 (t) A og up 2. 6 Char pol of A i det CA-21) 3 a (a-) g dn del 13 Nul Null (A-) -Span 3 2. Correspending Eigenvect oo 3 3 1:3 Null (A) Null - 2 13 Eigenvector Conrespinding (ser) YCH

e will fad Sof of Particula c X = L: 3 et Fundamental mabix 2 et X : -3et 2 et - et R pg ug Now FOD F F ie 6 set 3 So X 9dt X-J ESE 3 et 2 et -11t-1S -l1t-1o So is So Ct) 1 t- Y(th -t-l