ECE-205 : Dynamical Systems
Homework #2
Due : Thursday September 16 at the beginning of class
1) Problem 2.5 from the Notes
2) Problem 2.6 from the Notes
3) For each of the following first order differential equations, use an integrating factor to write
()yt
as a
function of its initial value
0
( )yt
and an integral of the input (plus some other functions)
1
( ) ( ) ( ) ( ) ( ) ( 2)
2
1
( ) ( ) ( ) ( ) cos( ) ( ) ( )
t
ay t by t cx t y t ty t x t
y t y t x t y t t y t e x t
t
Answers:
22 22
00
00
0
00
( ) ( ) ()
00
sin( ) sin( ) sin( ) sin( )
000
( ) ) ( ) ( ) ) ( 2( ( 2
((
)
( ) ) ( ) ( ) ) ( )
bb
t t t tt t
a
tt
t
a
tt
t
t
t
t
t
t
c
y t e x d y t e x d
a
t
y t e y t e
y t y t ey t x d y t e e x d
tt
4) Show that the governing differential equation for the following circuit is given by
2( ) ( ) ( ) ( ) ( )
b
b a b b a b
a
R
C C y t R C C y t y t x t
R
R
and that for this circuit
1
n
b a b
R C C
,
2
ab
ab
CC
CC
, and
b
a
R
KR
