Question

Exercise 4 Solve the IVPs by the Laplace transfrom. y' - - 6y = 0, y(0) = 11, y'(0) = 28 y" – 4y + 4y = 0, y(0) = 8.1, 7(0) = 3.9

Answer 1

@yu_yl_by zo Now using Laplace tramfom mehere , &(s)=L(*) ŜYU) – 5.yco) - y'vo) - ( $.465) -4 (0)) - 6 Y(S) 20 2) Š S)-115-28 -SY(3) + 11 – 6Y15) 70 = Y(3) - ( $$-5-6) = 115 +17 a Y (3) z ust 17 . 11s +17 5 s-6 (5-3) (3+2) 2 115122-5 (5-3) (312) 2 4 4 3 - 6-3) (3-2) s-3 S-3 2 US 3 + 1 ze + S ::Y6572 Taking Laplace inverse tromformination me hare ['(yes) 2 (62) 457 ( ya) 76.23X +5 824 - Solution yen) z 6. 634 5e2t

yol-4y'+44 20. y60) = 8.1, 4160723-9- Taking Laplac tromformation , 8(6)=L(%(%) Š4632 - Boyco) -yh(0) -4 SY(3) +470 +4.463)zo 29 Y05 h 57245+47 – 8.15 –319 +32.4 20 a Y() = -8115 +28.5 1. 5"-4574 -8.13 +28.5 (S-2)2 - 8.15 + 16.2 712-3 (5-2)2 2 -8.1(3-2) (3-2/2 12.3 (3-2) - -8.1 5-2 12.3 (3-2)L Taking inverse Laplene tranformation me fare L'819) 7 28.1. I' () - 12.3 E (6-ang 31 y 6) 2 -8.1 83% +12.3.4.2 The solution is g (122-811 12 + 12.30 e