Old Final Exam Solutions
1. y = Ae-cos
x
2. y = 3x + x-1/3
3.
|
n
|
xn
|
yn
|
f(xn,
yn)
|
yn+1
= yn
+ h·f(xn,
yn)
|
Error
|
| 0 |
0 |
1 |
0 |
1 |
.2840 |
| 1 |
0.5 |
1 |
1 |
1.5 |
1.218281 |
| 2 |
1 |
1.5 |
|
|
|
4. Linearly Indepent
5. y(x) = A + Bx + Ce4x
+
Dxe4x
6. x(t) = 13 cos(6t -
alpha), alpha = arctan(-12/5) + 2Pi
7. y(x) =
(5/2)e-x
- (8/3)e-2x
+
(1/6)ex
8. y(x) =
(1/6)ex
9. x(t) = -Ae-t + Be3t
y(t) = Ae-t + Be3t
10. x(t) = -e-t + 4e3t
y(t) = e-t + 4e3t
11. r(t) = (-1/8) + (17/24)e4t+(5/12)e-2t
12. F(s) = 6s/(s2+9)2
13. y(t) = u(t-2)((-1/8) +
(1/72)e8(t-2) + (1/9)e-(t-2))