PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 361

R.4.113 To gain additional experience, fi ve examples of DEs are presented and solved

manually, using the LT technique.

The following examples are solved for y(t) for each of the given DEs.

a. Example (#1)

Given the DE

240 020

dy t

dt

yt y

()


() with IC (initial condition) ( )

ANALYTICAL Solution

Taking the LT of the given equation results in

22040[()sY s 
Y s ] ()

sY s() 20 4 Ys() Ys()

2

 2

then

sY s()^2200 Y s() 

Ys s()(^2200 ) 


then

Ys

s

()
^20

 (^2)
taking the ILT
yt e ut
()
20 ^2 t ()
b. Example (#2)
Let the initial value of DE be
dyt
dt
yt
2
2 4

()

 ()

with the IC given by

y

dy t

dt t

()

()

00 

and 
 0 8

ANALYTICAL Solution

Applying the LT to the preceding equation

sYs sy

dy t

dt

Ys

t

2

0

() ( ) 04

()

 ()

sYs s Ys

(^2) ()
( ) 084 ()