Question

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(1 point) Find the most general real-valued solution to the linear system of differential equations ' x1 () = C1 + C2 x2(t)

Answer 1

Given el - 2 20 - 1 -4 ut O E 4 Find A values Now of ei gen >> (A-I ) - 0 ㅂ - - 0 -A- (4+4) (0+2) + 1 = 0 - 2²+67+ g = 0 T (+372 ㅋ -3, -3 Now eigen vector consider A-II A +3I - 1

Sove (A +31) * = 0 Augmented matre lo R2 Re&R I 15 0 0 21 (t) = X(t) x, (t) xalt) - xlt) 1 ut M2 It) = 1 A eigen ve cor 11

Now :):):) T e,te = (e, te) = 1 al का eite, - - 1 e = rei ei е : l. - loe, put e, e (:) Xt) с е *** (1) * 03 fee** () +33(0)) 3t Lt) - 3+1 ě 3 t + C2 -t te -3t - е è 3t 3t - te 3t att) +C2 Xyle) 3t e te 3 - e-3t