PROBLEMS: Section 3.3 For Problems 1-10, a differential equation and one solution are given. Use d'Alembert's reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? Differential equation 1. y" - y = 0 2. y" + y = 0 3. " - 4y'+ 4y = 0 4. " +y' = 0 5. " +y' = 0 6. xy" - 2(x + 1)y' + 4y = 0 7." - 6y = 0 8. x²y" - xy' + y = 0 9. (²+1)y" - 2xy' + 2y = 0 Solution Y₁(x) = et y₁(x) = sin x y₁(x) = ²x y₁(x) = 1 y₁(x) = 1 y₁(x) = ²x Y₁(x) = x² y₁(x) = x y₁(x) = x
PROBLEMS: Section 3.3 For Problems 1-10, a differential equation and one solution are given. Use d'Alembert's reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? Differential equation 1. y" - y = 0 2. y" + y = 0 3. " - 4y'+ 4y = 0 4. " +y' = 0 5. " +y' = 0 6. xy" - 2(x + 1)y' + 4y = 0 7." - 6y = 0 8. x²y" - xy' + y = 0 9. (²+1)y" - 2xy' + 2y = 0 Solution Y₁(x) = et y₁(x) = sin x y₁(x) = ²x y₁(x) = 1 y₁(x) = 1 y₁(x) = ²x Y₁(x) = x² y₁(x) = x y₁(x) = x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can you please show an easy way using d’Alembert's reduction of order method to find a second linearly
independent solution. What is the general solution of the diferential
equation for number 7
Transcribed Image Text:PROBLEMS: Section 3.3
For Problems 1-10, a differential equation and one solution are given. Use
d'Alembert's reduction of order method to find a second linearly
independent solution. What is the general solution of the differential
equation?
Differential equation
1. y" - y =0
2. y" + y = 0
3. " - 4y'+ 4y = 0
4. " + y = 0
5. " + y = 0
6. xy" 2(x + 1)y' + 4y = 0
7.¹" - 6y = 0
8. xy" xy' + y = 0
9.(²+1)y" - 2xy' + 2y = 0
Solution
Y₁(x) = et
y₁(x) = sin x
y₁(x) = ²x
y₁(x) = 1
y₁(x) = 1
y₁(x) = ²x
y₁(x) = x³
y₁(x) = x
y₁(x) = x
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