Solutions for Chapter 4
Section 4.1
(18) Sol: Note that the frequencey in cos t is ! = 1:Set
cos t
sin t = A cos (t
)
Dierentiate both sides,
sin t
cos t =
A sin (t
)
Let t = 0; we nd
1 = A cos
1 = A
Solutions for Chapter 1
Section 1.2
0
(2) LHS = y0 = (3t + t2 ) = 3 + 2t
1
1
RHS = y + t = (3t + t2 ) + t = 3 + t + t = 3 + 2t
t
t
* LHS
RHS
) y = 3t + t2 is a solution
(10) y 0 =
p
t
; the general so
Solutions for Chapter 3
Section 3.1
(8) (DC)T =
1 6
1 7
1 1
; B =
1 0
(24) Counterexample: A =
(A + B) (A
2
0
1
: Then A2
1
B 2 6=
B) ; because
(A + B) (A
B) =
A2
B2 =
3 6
;
0 1
2 1
1 1
4
0
3
=
1
2 4