Math 181/281. Rumbos
Spring 2011
1
Solutions to Review Problems for Exam 1
1. Show that the IVP
dx
= 3x2/3 ;
dt
has more than one solution. Explain
x(0) = 0,
why this result does not contradict the local existence and uniqueness theorem
proved in class.
S
Math 181/281. Rumbos
Spring 2011
Page 1
Solutions to Assignment #9
1. Let A and Q be 2 2 matrices, and assume that Q is invertible. Suppose that
x
x
(x(t), y (t) is a solution to the system
=A
. Show that by making
y
y
x
u
, we obtain a solution to the sy