Name________________________
Student I.D.___________________
Math 2250-4
Quiz 11 Solutions
April 13, 2012
1a) Use the methods we've been discussing to find the general solution to the system of differential
equations
x# t
=
y# t
0
1
x
K6 K5
y
.
(8 points)
0Kl
K6
1
K5 K l
2
= l lC5 C6 = l C5 lC6 = lC3
l =K3 the homogeneous system is
3
1 0
K6 K2 0
l =K2 the homogeneous system is
2
1 0
K6 K3 0
/
/
3 1 0
0 0 0
2 1 0
0 0 0
0v=
0v=
lC2
1
K3
1
.
K2
Thus the general solution is
x t
y t
= c1 eK2 t
1
K2
C c2 eK3 t
1
K3
.
1b) For any solution x t , y t T to the first order system of DEs above, what is the second order
differential equation satisfied by x t ?
(2 points)
The first order system reads
x# t = y
y# t =K6 x K 5 y .
Thus x##= y#=K6 x K 5 y =K6 x K 5 x# . We can also write this DE in the usual form for an unforced
undamped mechanical or electrical system
x##C 5 x#C 6 x = 0 .