## Description

Homework #9 Math 527

Problems 1-6. Find the general solution of the system of equations. For problems with

complex eigenvalues, express your answer in both complex and real-valued form. Prime

notation means differentiation in t, i.e. x

0 = dx/dt.

1. x0 = x + 2y

y

0 = 4x + 3y

2.

x

0

y

0

=

−4 2

−5/2 2 x

y

3. x0 = x + y

y

0 = −2x − y

4. x0 = 5x + y

y

0 = −2x + 3y

5.

x

0

y

0

=

−1 3

−3 5 x

y

6. x0 = 12x − 9y

y

0 = 4x

Problem 7. Solve the initial value problem.

x

0 = −3x − y, x(0) = 3

y

0 = 9x − 3y, y(0) = 5.

Most problems adapted from Section 8.2 of Zill’s “First Course in Differential Equations,” 9th edition.