Math 2552 – Differential Equations Worksheet 7 (Jan 30, 3.3,6.3)
Georgia Institute of Technology, Spring 2019 Systems, Distinct real eigenvalues
For each of the following systems, find the general solution, draw a phase portrait, and
classify the fixed point. If an initial value is given, also solve the initial value problem.
1. x0=1 1
4−2x
2. x0=−2 1
−5 4x,x(0) = 1
3
3. x0=3 6
−1−2x
4. x0=
−1 0 3
0−2 0
3 0 −1
x,x=
2
−1
2
(note: On number 4, only solve. The phase portrait is in 3 dimensions and difficult to
draw.)
1
