Question

MAP2302-20Summer 2003 Homework: Homework 11 Score: 0 of 1 pt 6 of 1 X 7.6.28 Solve the given initial value problem using the method of Laplace transforms. y'' + 5y + by = tu(t-3); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem. ials y(t) = 6 -21 -31+ 13 36 e t-3 6 -211-3) 5 4 -3(-3) + e + 9 е u(-3) ces Question is complete. Tap on the red indicators to see incorrect answers. All parts showing ations Materials - Previous aterials ss Resources 25 IV A 000

Answer 1

Problem- Ginen Pup is- Y"+sy't by tult-3) 440)=0, y (0)=1 Taking laplace both side- [sy(s) - 5460) -4'03 ] + 518465)-Y(0)] +645) = 384_)e-3 ) -35 put initial wilhe- sy()-1 +58448) + 6405) = (3$++)e-35 463) (32+55+6) 1+ 138+1 52 -35 YCS) = + (38+1) e-35 (5+2)(5+3) 52(8+2)(5+3) 5 yes) = 543 + + 13 365 S+2 4 - 1188+2) 3») 9(2+3) 13 e-35 Taking inverse laplace both side- Y(t) e-2t _ é 3t t-3 ( Se-266-3) + B.-316-3) 6 4 36+

Problem-2 Ginen initial walue problem- wil 6W+9w=18++51, W1-1) = 4, w(-1)=2 let a=t+1=) t-a-l Then w"(a-1) -Gwila-1) +qw1Q-1) = 1810-1)+51 and wth) = 4, wl($)=2 > Now, to simplity life a little let's definel- U141) = Hola-1) 3) ua) = wi(0-1) ullca)= wllla-1) How equation will be- U"(a)- Gul(a) +qu(a)= 180 +33 VIO) = 4, ulco)=2 $?$(8) – 544-2) -65U (8) +24 + quess 18 33 SI+ S (52+65 +990(s) — 45 +22 = 18 52 33 S 152_65+9) UCs) = 18 + 33+ 45-22

UCS) = 18 33 S2(S-2)2 5(5-32 + 4.5-22 (5-32 UCS) = 18 +335 + 483 - 2252 S²(5-3)2 Partial traction- + są +29-e-39 3 UCS) = 2 2-st (5-32 Taking inverse la place- uca)= e-39+ 306 30 Now purt u(t+1) = 5+ 2++2-et31t+1)+316+1+3LHD W(t) = = 7+2+ + 314+1) et34+)2 +31+1) wolt) = 7+2+ + 3% e 316+1) + a = tt 1 е. +2e3(t+1)