MATH 2280-002 Exam 1 Extra Credit ( #9 )
Math 2280 Section 002 [SPRING 2013]
Instructions: This is extra credit. It’s optional and won’t hurt your grade whether or not you attempt it. The points you score on this assignment will be used to augment your score on question
#9 of Exam 1. Regardless of how well you perform on this assignment, you will be allowed to score at most 7 out of 10 points on #9 . In other words, if you scored 4/10 on #9 , you can earn at most
3 points on this assignment. I have indicated how much each problem is worth so that, if you do not need many points, you will not need to do as much work. You can attempt as many problems as you like.
This assignment is due in class on Friday, April 12. You will receive either full or no credit on each problem. I will be grading more harshly than usual because this is extra credit and I’m anticipating a lot of questions to grade. If you don’t show enough work, you will receive no points. You need to convince me that you didn’t just plug the differential equation into Maple or copy another student’s work. If your work is too messy for me to follow easily, you will receive no points. Be sure to clearly indicate your final answer. Don’t included unrelated scratch work.
For problems 1-9, solve for y
( x
) using the method of undetermined coefficients.
1. ( 1
3
2. ( 1
3
3. ( 1
3
4. ( 1
3
5. (
1
3
6. ( 1
3
7. ( 1
3
8. (
1
3
9. ( 1
3 pt) y
′′
−
7 y
′ + 12 y
= 864 x
2 pt) y
′′ + y
= 6 cos( x
)
+ 144 x pt) y
′′ + y
′
−
12 y
= 130 sin(2 x
) + e
− x pt) y
′′ + 4 y
′ + 4 y
= e
− 2 x + x
+ 3 pt) y
′′
− pt) y
′′
−
3 y
′
−
10 y
= 75 sin( x
) e
6 y
′ + 25 y
= sin(4 x
) e
3 x
5 x
+ x cos(4 x
) e
3 x pt) y
′′
−
3 y
′ + 2 y
= 2 xe x ; y
(0) = 1 , y
′ (0) = 2 pt) y
′′
−
6 y
′ + 9 y
= xe
4 x + 5 e
4 x ; y
(0) = 0 , y
′ (0) =
−
10 pt) y
′′
−
2 y
′ + 4 y
= e x + 12 ; y
(0) = 2 , y
′ (0) = 3
For problems 10-17, solve for y
( x
) using variation of parameters.
10. (
1
3
11. ( 1
3
12. ( 1
3
13. (
1
3
14. ( 1
3
15. ( 1
3
16. (
1
3
17. ( 1
3 pt) y
′′ + 8 y
′ + 15 y
= 16 e
3 x pt) y
′′ + y
= 6 cos( x
) pt) y
′′
−
3 y
′
−
10 y
= 75 sin( x
) e
5 x pt) y
′′ + y
= tan( x
) pt) y
′′ + 9 y
= sin( x
) cos(3 x
) pt) y
′′
−
3 y
′ + 2 y
= 2 xe x ; y
(0) = 1 , y
′ (0) = 2 pt) y
′′
−
2 y
′ = x
; y
(0) = 0 , y
′ (0) = 0 pt) y
′′ + 2 y
′ + y
= e
− x ; y
(0) = 1 , y
′ (0) = 4
18. ( 2
3 pt) Solve the initial value problem x
′′
−
3 x
′ = 6 + 12 e t
, x
(0) = 1
, x
′ (0) = 4
.
using the method of undetermined coefficients.
1

MATH 2280-002 Exam 1 Extra Credit ( #9 )
19. ( 2
3 pt) Solve the initial value problem x
′′
−
3 x
′ = 6 + 12 e t
, x
(0) = 1
, x
′ (0) = 4
.
using variation of parameters.
2