PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 363

ANALYTICAL Solution

Taking the LT of the given equation

203

30

sY s y Y s

s

 () ( )
()

Ys s

s

()[ 23 ]

30



then

Ys s

s

()( 23 )

30



Ys

ss ss

A

s

B

s

()

()(.).
















30

23

15

(^1515)
by partial fraction expansion
Ys
ss
()
.



10 10
15

then
yt()
£ [ ()]Ys
 1
and
yt ut e ut
()
10 () 10 ^15 .t()
e. Example (#5)
Let
dy t
dt
yt

()


40 ()

with y(0) = 10.

ANALYTICAL Solution

Taking the LT of the preceding equation

sY s()^104 Y s()
^0

Ys s Ys

s

()(
) , ()




410

10

(^4)
and
yt()
£ [ ()]Ys
 1
then
yt e ut
()
10 ^4 t()
R.4.114 The MATLAB function F = laplace(f) returns the LT of ƒ, denoted by f(t) → F(s),
where f is a symbolic object with independent variable t.