Question

sokmarks UCF Canvas MUCH Knights Email Cengage Homepage - UCF. Mathway Trigono... = MAP2302-20Summer C003 Modules > Student's Pearson Links > MyLab Math Gradebook MAP2302-20Summer 2003 Summer 2020 Home Review Homework: Homework 10 Announcements 6 of 10 Discussions Score: 1 of 1 pt 7.5.12 Grades People Files Solve the initial value problem below using the method of Laplace transforms. w"-w' + 9 = 18+51, wf-1)=4, w'-1) = 2 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms wit) - 2,5+213(3+3+21+ 7 (Type an exact answer in terms of e) Course Materials ndar Zoom 213 Syllabus box Quizzes Modules Help Conferences Collaborations Question is complete All parts showing Chat Adopt Materials Buy Materials Previous TV $ 8 1 2 3 4 5 8 CO W E R T Y А S D F G H

Answer 1

- 2 WlGw't gw = 18 + + 51 W(-1) = 4 w'(-1) = 2 Son: Let us define, v(t) = q (t-1) y"(t iwt-1) =VCE) and w' (t-1) = VCt). We get the new IVP, V! - G V1 + 9 V = 18.(t-1)+51 = 18 t -18 +$ 1 V"-ortov - 18 t +33 with VCO) = 4 v'(0) = 2 To New IVP Taking Laplace transform both sides, vil +46) (s V-V1_) + 9V I=0 of الای - 27ی t=0 + 32 52 S sev 65V + 9 = 18 S2 + 33 + 45 +2 +664) s vise 6s+ 9) = 18 45+ 26 33 S + S2 DV = + 33 $?($2_65+9) + us s(s2_6549) 526549 + 26 5² 65+9

Page No Date 18 133 45 t 26 V= S2(3-3)² s(8-3)? '. (5-3) (-3) ?

AstB + + 18 s ² (3-3)? JO 2 S2 (5-3) On solving, tez (AS+B) 5-3)2 + (9-3) + Ds : As +B) (3²-6s+ 9) + (5²-366 + Ds - As3-6AS²9 As +Bs²_GBs + 9B + Cs? +Ds3Cs =As3+ (-6A +B+C)52 +84-6B +D-30)5 = 2 18 + 9B On equeting, 9B = 18 B=2 JA=0 GA +B+C =0 as CE 6A-B = -2 C=-2 GA-6B+ D-3C =0 D = 30 +6B-9A=-6 +12 = 6 D-6 = A B + 33 S(8-3)2 S (5-3) (5-3)2 33 A(5-3)2 + B 5(5-3) +cs = A/s2-65+9) + B/s2_38) + c A+B)52+ (-6A - 3B+C) s + 9A 9 A-33 -GA- 3B+c=0 A-11 3 A+B=0 Be-11 3 C=69) +36) C-22-11-11

4s + (5-3)2 S-3) (5-3)² 45 = A(8-3) + B 45 AS-3A + B = As+(B-3A) DA comparing A-4 B-BA = 0 B =12 26 A B + (5-3)2 (5-3) (5-3) ² 26 SAS +(B-32) B-3A= 26 B-26 A=0

finally V= 2 Ell) + s2 (2) 6 + +Il+ (5-3) S-3) (5-3)² 35 3(5-3) 12 4 26 F (5-3)2 (5-3)2 5-3) (5-3)? V on using inverse laplace transform V(t) = 2t - 2.23 + Gezt t til -11e3t +11.estt + 483t + 12e3t t +26e3tt 3t 3 3