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Homework #9 Math 527

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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.