Question

One solution of x' = The general solution is 2 2 x+ b(e) is x(+) = (47 12 e34 Сі + C2 + ОВ. е“ e3t С1 + C2 + C3 e3t Int et Сі + C2 + C3 e3t In D. et est C1 + C2 + est Int OE Int

Answer 1

Let A (2] Eigenvalues of A: IA-AI! -0 =) 2-4. 1 . - DE । 2-1 = (2-4)2 -1=0>) 4+4+41-150 s.22-44 +3=0 -10-01 1-3)=0 > a = 1,3 Lee », =l, az = 3 It d, 31, then [Anth, IJ V, -0 => [A - FJ vi=0 >>[:@:) -[:] » [!] - X, tx2 -0 = x, =-22 Take &q=1 VE .:.*, ay (5:1=[:)] If Az = 3, then (Ari, I ) V2=0 =)[A-31]V, = >> 4618 16:1-[:] =)

>g,-?, so =), = 32 Take B₂=1 2,- - V2 2:1=[:] Xc (E) = λι Ε Cle el Net vi tee en 3 + Xelt) = Ciet [1']+2. é [1] t е. e iz) X(t) = a ()5+1 نے et ė ) option {