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5

hiL(t) e tsin2t (t)

2dh1d5

huL LiL ×[e tsin2t (t)]

dt5dt2

1

[ e tsin2t (t) 2e tcos2t (t)]2

1 t t

[ecos2t esin2t] (t)

2di

uL LL

dt

dhiL

dt

y 2y f (t) f(t) huL L

H(p)

2．8 （1）

p 1p 2 33

1 p 2p 2p 2

2t

t

t

t

h(t) (t) 3e (t)

3

g(t) h( )d ( )d 3 e 2 d (t) (1 e 2t) (t)

0o02

（2）y'(t) 2y(t) f''(t)

p2p2 2p 2p 4 44

H(p) p 2

p 2p 2p 2

h(t) '(t) 2 (t) 4e 2t (t)

g(t) h( )d '( )d 2 ( )d 4 e 2 d (t)

0

0

0

0

t

t

t

t

(t) 2 (t) 2 (t) 2e 2t (t) (t) 2e 2t (t)

2.9，求h(t)

(1) 2y'' 8y f H(p)

12p2 8

11

2p2 4

1

h(t) sin2t (t)

4

(2) y'' y' y f'

f

111 p

p 1 H(p) 2

p p 1(p )2 (p )2 2424p