MATH 411 HOMEWORK 3
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411hw3su14.pdf
MATH 411 HOMEWORK 3
1. For the following equations,
• Find the general real-valued solution. • Classify the equilibrium at the origin. • Sketch a phase plane diagram.
(a) x′ =
( 2 2 2 −1
) x
(b) x′ =
( 1 1 −1 1
) x
(c) x′ =
( 0 9 −9 0
) x
2. Find the general solution to
x′ =
3 0 40 2 0
0 0 −3
x
3. Solve the initial value problem
x′ =
( 1 3 3 1
) x, x(0) =
( −2 1
) 4. Find the general solution (using either of the methods we discussed in class) for
x′ =
( 2 1 −9 −4
) x
5. Find eAt for each of the following matrices:
(a) 2 −2 20 1 1
−4 8 3
(eigenvalues are 1, 2, and 3)
(b) 1 1 00 1 0
0 1 1
(you can do this without using the Putzer algorithm)
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