+(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. + 2y differential equation. In each of Proble Xy" - 2y' - 3y = 3e²¹ Determ 2. y" - y' - 2y = -2t+4t² undetermin N b. Use of the giver 4. 3. y"+y'-6y = 12e³t+ 12e-2t y"-2y' - 3y = -3te-t y" +2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-¹ ✓ "! I 3 in (2011 (24) 16. 17. y"-5y' - H 18. y" +2y' - y" + 3y': H
+(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. + 2y differential equation. In each of Proble Xy" - 2y' - 3y = 3e²¹ Determ 2. y" - y' - 2y = -2t+4t² undetermin N b. Use of the giver 4. 3. y"+y'-6y = 12e³t+ 12e-2t y"-2y' - 3y = -3te-t y" +2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-¹ ✓ "! I 3 in (2011 (24) 16. 17. y"-5y' - H 18. y" +2y' - y" + 3y': H
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
13 pl
Transcribed Image Text:by 1.
be
If the nonhomogeneous function involves both cos(3t) and sin(ßt), it
convenient to treat these terms together, since each one individually may give rise
form for a particular solution. For example, if g(t) = t sint+2 cost, the form for
Y(t) = (Aot + A₁) sint + (Bot + B₁) cost,
provided that sint and cost are not solutions of the homogeneous equation.
Xy" - 2y' - 3y = 3e²t
2. y" - y' - 2y = -2t+4t²
Problems
In each of Problems 1 through 10, find the general solution of the given
3.
4.
5.
6. y" +2y' + y = 2e¹
بود
y"+y' - 6y = 12e³t + 12e-2t
En 97
y"-2y' - 3y = -3te-t
y" + 2y' = 3 + 4 sin(2t)
7.
y"+y = 3 sin(2t) + t cos(2t)
nogo 200
8. u" + wu = cos(wt), w² #wo
9.
3. u" + w₁u = cos(wot)
ials by t to increase th
(20)
15. y" +2y +
al solution of In each of Proble
Determ
undetermin
N b. Use a
of the given
10. y” +y+4y = 2 sinh t
Hint; sinh t =(e – e-)/2
In each of Problems 11 through 15, find the solution of the given initial
value problem.
11. y"+y' - 2y = 2t, y(0) = 0, y'(0) = 1
12. y" + 4y = 1² +3e¹, y(0) = 0, y'(0) = 2
13. y" - 2y + y = te' +4, y(0) = 1, y'(0) = 1
14. y" +4y= 3 sin(2t), y(0) = 2, y'(0) = -1
16.
y" + 3y' =
17. y" - 5y +
18. y" +2y +
19. y" + 4y =
20. y" +3y' +
y" +2y +
21.
22.
Consider th
from Example 5
solutions of the c
method of reduc
nonhomogeneous
where v (t) is to b
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