Question

Use Laplace transform techniques to solve the following; a = x + y - 9t, x(0) = 1 a ly = 4x + y, y(0) = 4 b) sinh(t) = S. y(z) cos(t – z) dz

Answer 1

clusions ① dia aty.gt - ERN - 44444 Yo=4 writingegno, d ty-94 (Let [X(t) = XL): and £[yet)] = 718) :) Operating hopes operator of both side, * )[14794) = 4(246) 2 [yet) - 94[+] · X (2) - 110) = X) + y(s) - q - - Sirialy Laplace sproster operating bomsides in , we 460-ylos = 44443) 4440): - Bom ④ 2② written as, ç (24) 40 -41): 1-%2_x_4e 4 X13):4 (54)448)= 4 x 418+74137 - 4418) = 4-36,7 - 4114) X(B) =(3+)? 41s)--4787) - ((84)?-4 )400) = A=248 + 4csx) 7 ${(84)*–4} 400 E 48-34 6- 42 - 36 ZZZ22222241471111 160024 (BH) 6-3): . VERTER Scanned with CamScanner

MIRROR 418724 (8+1) (-3) 82(6+1) 1)-3): C YA 36(8-3) 98 418+1) 3282 ? e German 4182=8 -05-12 s jete pé-8=122. © Pulting. ① in ②, we have. ad (dé-0-12+) = 44214+ (De-0-124). 8 et 12 - 4aith of det - 8-12t a thet 121-4 =4214) 20. -46 +3t-1.- © alt= -4 etatt y th= det 8 + 2t solution of system . $canned with GamScanner

AZE convolution ! 6 Sinhit = yen coslt-2) di operating bom side Laplace and uring definition of Using convolution theorem) Link (03- 4 () * c1) = £[yeo] L [cost]. .. 8 St. Llyen). 8 (81) & fryen] = $18+126811_ 8611)(81) á xes] = s st 2[n) t woice to aldrigisu 4 3 4 1 2 3 * stan 13 t & yen= et et 1. yeo a q cosh Lt) -1. Scanned with CamScanner