Question

Task 3. Solve the following nonhomogeneous equations using the method of undetermined coefficients. IO 1) (0) (a) · = x + ( ); x(0) = (0,0). 1-1 -2) . It Hint: to find a particular solution, substitute x(t) = tv1 + V2 where V1, V2 are constant vectors, and find conditions on V1, V2. 1-1 1 11 10 (b) <= 10 -1 1 x + 10. 1 0 0 1 ) (0) +- + 1)--) (ezt

Answer 1

03.02. To --2 2(o)-(60) - er genvalue 1-2 (220-2-7)+1=0 2 +20+1=5 7 = -1, -1 so it) - Ciet & Cat et 2 (t) = x (t.) a(t) = -c, et tet la tet so Alght) = (C., - c. ) et - catet Now for particular solution xp (t) = 1 atbt T Ctdt tron a+bt +ot J L-12C I C+ dt I-a-bt-factadt) +t b = c 1 = -(a+ac d=0 80-2 c = a

Page No Data: 0 sinced=0 +20 + 1 = b = 1 a = 2 alt 1 - 2 tt X(t): Joget te te t - 2+t 1 [c2-cije - latet & 2(0) TC-2 19-ati - C. - - 24 so alt) = ttet -2+t - 1 g +1