Online Quiz #5
Find the general solution:
1. y 00 + 4y = −4 tan 2x
1
2. y 00 + 4y = −4 sec 2x
2x
e
3. y 00 − 4y 0 + 4y = −4e2x +
x
2x
e
4. y 00 − 4y 0 + 4y = −4e2x + 2
x
5. y 00 + 4y = −4 cos 3x + 2 sin 3x
6. y 00 + 36y = −4 cos 6x + 3 sin 6x
7. y 00 − 2y 0 − 8y = 2e−2x + 3
8. y 00 + 4y 0 + 4y = 4xe−2x
9. y 00 + 4y 0 + 4y = e−2x cos x
10. y 00 − 2y 0 − 8y = 2e−2x
11. y 00 + 2y 0 = 4 sin 2x
12. y 00 − 3y 0 − 4y = 2x + 5
13. y 00 − 5y 0 + 6y = x3 + 3x
14. y 00 − 2y 0 + 10y = e−x sin 3x
15. y 00 + 2y 0 + 10y = e3x cos x
Find the solution of the initial-value
problem.
16. y 00 − y 0 − 6y = 3x,
y(0) = 1, y 0(0) = 2
17. y 00 + 4y = x2 + 5ex,
y(0) = 0, y 0(0) = 4
18. y 00 − 3y 0 + 2y = sin x,
y(0) = 1, y 0(0) = −3
Give the form of a particular solution.
19. y 00 − 2y 0 − 8y = 2 cos 3x − 3e−2x − 3
20. y 00 + 4y 0 + 4y = e4x sin 2x + 3e−2x − 3x