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...
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Questio. 6 please
Transcribed Image Text:104
Chapter 4
Linear Second-Order Equations
4.2 EXERCISES
In Problems 1-12, find a general solution to the given differ-
ential equation.
1. 2y" + 7y' - 4y = 0
3. y" + 5y' + 6y = 0
5. y" + 8y' + 16y = 0
6y"+y' - 2y = 0
7.
9. 4y" - 4y' + y = 0
11. 4w" +20w' + 25w = 0
12. 3y"+11y' - 7y = 0
2. y" + 6y' +9y = 0
4. y" - y' - 2y = 0
6. y"-5y' + 6y = 0
8. z"+z' -z = 0
10.
yy'- 11y = 0
I
In Problems 13-20, solve the given initial value problem.
13. y" + 2y' - 8y = 0; y(0) = 3, y'(0) = -12
14. y"+y' = 0; y(0) = 2, y'(0) = 1
15. y" - 4y' + 3y = 0;
16. y" - 4y' - 5y = 0;
17. y" - 6y' +9y = 0;
18. z" - 2z' - 2z = 0;
19. y" + 2y' + y = 0;
y(0) = 1, y' (0) = 1/3
y(-1) = 3,
y(0) = 2,
y'(-1) = 9
z(0) = 0,
y(0) = 1,
20. y" - 4y' + 4y = 0;
y(1) = 1,
y'(0) = 25/3
z'(0) = 3
y'(0) = -3
y'(1) = 1
21. First-Order Constant-Coefficient Equations.
(a) Substituting y = e", find the auxiliary equation for
the first-order linear equation
ay' + by = 0,
where a and b are constants with a # 0.
(b) Use the result of part (a) to find the general solution.
In Problems 22-25, use the method described in Problem 21
to find a general solution to the given equation.
22 31' 7-0
0
In F
func
27.
28.
29.
30.
31.
32.
33.
34.
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