Question

use the Laplace transform to solue the initial value problem y - 3y +2y = h (t) Y(o)=0 yo(o)=0 where h(t): 0,0 Lt L4 t> 4 { 2

Answer 1

Given Dit 4" - 3y'+zy het) 0,410 = 0 , 4'162=0 taking laplace trasform on both sides 174"(H) - 3L24'6") } +21946+3 = 1 { het) 2 we knew 134"(+)3 = 5?1346773 - 54(0)-40) L?y"(t)} = s?L? y(t) } 1 ?'u2 3 = 517473-410) 1 {y'C+?} = 5!?y(+) 3 egn © be comes s'l{4(t)} – 351244173 +213447)} =[ { het} (52-35+2 ) {{44)} = 1 {het) }

Oct 24 OS het): ind 2 t>4 By defn. 1984 1983 1984 4 st est coldt + Szést at 4 75. Jos TP = 2 st e 15. [ 4 cost -45 + e S Totes ] 1 ?net13 - zes : (82-35+27 1 2 4473 - zés ze shat = {innel S (52-35+2) -45 ze 124413 515-1115-2)

ë 4 s 4(H)=11"} ;} 5(5-1(5-2) we. partial fraction C B + 1 A + (5-2) s (5-1) 5(5-1)(3-2) - A15-1)(5-2) + B 5(5-2) + (561) Put so A (-1)(-2) A = = - put 5-1 B (1-2) B - put 5=2 1 - 20(2-1) can

45 45 Yu) = 2 f? 3-13 es 3 12 cs (4-2) - Y47 2 ( ) 1 Ut-4) e U{-4) + 2 (14) e c-457 2 2 All) - ( - - (-) 2 (4-4) 2e fe the solution of initial value. problem.