Page 239 - Engineering Mathematics Workbook_Final

Laplace Transforms

57. The solution of the differential
equation, for t > 0,

'' y ( ) 2 't + y ( ) t + y ( ) 0t = with

initial conditions y(0) = 0 and y’(0) =
1, is? (u(t) denotes the unit step

function),

( )
t −
(a) te u t
t −
u
(b) (e − te t − ) ( ) t

−
u
(c) ( e + t − te t − ) ( ) t
( )
t −
(d) e u t [GATE-2016]

58. The Laplace transform of

n −
t 
f ( ) t = t e u ( ) t is

(n + ) 1 ! ! n
(a) n+ 1 (b) n
+
+
(s  ) (s  )

(n − ) 1 ! ! n
(c) n+ (d) n+ 1
(s  ) 1 (s  )
+
+

[ESE-2018 (EE)]

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