TEXAS A&M UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 308-200
Final Exam, 10 Dec 2013, version A
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work.
Name (print):
In all questions, no analytical work — no points.
1.
Solve the initial value problem
xy 0 = 2y + x4 ex ,
y(1) = 10.
2.
Find the general solution of
x00 − 2x0 + 5x = sin 2t.
3.
Find the solution of the initial value problem; sketch the phase portrait of the system,
identify the type of the critical point at (0, 0)
!
!
−1
−4
1
x0 =
x,
x(0) =
.
1 −1
−2
4.
Find the general solution of the non-homogeneous system

x0 = x + x + 5e2t ,
1
2
1
0
x = 4x1 − 2x2 .
2
5.
For the nonlinear system

x0 = 3x − x2 − xy,
y 0 = 2y − xy/2 − y 2 ,
(3 points) find all critical points, (6 points) find their type, stability and sketch their local
phase portraits, (1 point) sketch the global phase portrait.
6.
Bonus question +2 points (no partial credit): Solve question 2 by a different method.
Points:
/30