MATH 251
Exam I
September 26, 2011
ANSWER KEY (Form A)
1. (a) No (b) Yes (c) No (also acceptable: Yes, it can be rewritten
into an exact equation because the equation is separable.) (d) No
2. D
3. A
4. D
5. A
6. D
7. B
8. A
9. B
10. D
11.
y=!4et2
+12
12. (a) y = 0, 2, 4 (b) y = 0 is (asymptotically) stable, y = 2 is unstable,
y = 4 is semistable. (c) 0 (d) 4
13. y = C1 t −2 + C2 t 4
14. (a)
yc=C1e9t+C2e!t
(b)
y=C1e9t+C2e!t!2t!4
9
(c)
Y=(At2+Bt )e!t+C e9tcos(4t)+D e 9tsin(4t)
