Question

Solve the initial value problem below using the method of Laplace transforms. y" - 2y' - 3y = 0, y(0) = -1, y' (O) = 17 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms y(t) = 1 (Type an exact answer in terms of e.)

Answer 1

Solution: Given that The initial value problem is Y" – 2y) – 3y=0; y(0)2-2, Y 17 we using the laklace pansform we have L{ yll_24' - 374 = {0} Lkyll}-LL2ylly - L434} = 0 L{ylly -2Lfyll - 3L47}=0 (52 LKY (H)} – 5 Y(0) – yllo)] -2[ SLELH) – 870] -3 L4143 substituting the value 420) = -1 and Y'(0)=17 7(52L414sx (+)–17) – 2[SLKYU– (-) – 344714=0 LxY64} ( 52 25 - 3] +5-17 - 250 L {44} [52-23-3) = -5 +19 - L441} = 15-7) (+)

- St19 (SH) (5-3) (S+1) & - st 19 1S+) 45 37 -StL9 A(5-3) +B(st) +)6537 (A+B) S-3A +B. = At= -2 1 3 AHB = 19 4A = -20 7 1A=-5 -5+B=- Leyet? = = 154 B=-115B-4] + 325

Take inverse lablare of equation of we have L { L 24 (4}} = Lt { is + 4 } 91 +) = N()+cente y = -5L{$+44745 y(t) =-5 et +4e3t Ans]