Question

Homework: 7.6 Score:0 of 1 pt 9 of 9 (6 comple X7.6.28 Solve the given initial value problem using the method of Laplace transforms. y'"+3y'+2y tu(t-2); 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. y)

Answer 1

All y'39' + 2y = t. ult-2) ? ylo) = o ; yo) = 2. As ult-2)= { ó ,t.>2 Holst ta24 : lutt-)) = 12418) dt jete po at + je*() at 2 Kinilit de (0-22) - & 4[tagit)) = (-1) & GLS) where Gla) = 6.19141) : 1/#ut) = (0,A( 161.4lt-2)) = 2ses 7225 you given differential Equation is yº+3y' +2y = 7:471-2) Taking Laplan Trand form on both sides, we get (- aģ1093 - ytos) + 3 a9- ym) + 2ğ = asetz24 7 (87° 410-1) +3(-5-0) +ag = ei tee 13)

7 (8ğ-1) + 319 + sỹ = odbe one 19 (3*3*ta) ; = 19 (8+31+2) - *200* 2 st 3) . ☺ 20 +280*4 + $ so (D+1)(8+2) Taking inverse Laplace transform on both sides, we get Sime 2" (as 19 am)) = 1"13+ weight ) . (using partial Fraction) --t)'? 14.)-414). ) ::"(saw),on) - -* *** ******* Law)- gale) ested 14)={10-2) et 16 , Town) ---Alt-) +9.4) 1867), en Loter h ISIA <2 Now

الم) ( - ) = (د ) out 12م) ا+A 2tم - tتم s from o -الح (دوره - - - - الفلق - (19)2 +3- = ( 22 - ا 28 - ام + 2-2 34 + 2 + 6 - و دي . - م - م - : (4)