8. Problem 5.3.1.12: x²y" + (a²x² – v² + ¿)y = 0, use y = vxu(x) %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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problem 8 just please using Bessel Functions
![**Problem 5.3.1.12:**
\[ x^2 y'' + \left( \alpha x^2 - \nu^2 + \frac{1}{4} \right) y = 0, \text{ use } y = \sqrt{x} u(x) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2140facb-0981-40cd-bf23-81e224855fc4%2Fa210bdd1-b234-4b9e-b775-84f00e04afed%2Fzvbscu_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 5.3.1.12:**
\[ x^2 y'' + \left( \alpha x^2 - \nu^2 + \frac{1}{4} \right) y = 0, \text{ use } y = \sqrt{x} u(x) \]
![**Problems from Differential Equations:**
Find the general solutions and use the indicated substitution for problem 8.
**7. Problem 5.3.1.3:**
\[ 4x^2y'' + 4xy' + (4x^2 - 25)y = 0 \]
**8. Problem 5.3.1.12:**
\[ x^2y'' + \left(\alpha x^2 - \nu^2 + \frac{1}{4}\right)y = 0, \text{ use } y = \sqrt{x}u(x) \]
**9. Problem 5.3.1.19:**
\[ xy'' + 3y' + x^3y = 0 \]
These problems involve finding general solutions to differential equations. In problem 8, use the substitution \( y = \sqrt{x}u(x) \) to simplify the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2140facb-0981-40cd-bf23-81e224855fc4%2Fa210bdd1-b234-4b9e-b775-84f00e04afed%2F6zsr9e_processed.png&w=3840&q=75)
Transcribed Image Text:**Problems from Differential Equations:**
Find the general solutions and use the indicated substitution for problem 8.
**7. Problem 5.3.1.3:**
\[ 4x^2y'' + 4xy' + (4x^2 - 25)y = 0 \]
**8. Problem 5.3.1.12:**
\[ x^2y'' + \left(\alpha x^2 - \nu^2 + \frac{1}{4}\right)y = 0, \text{ use } y = \sqrt{x}u(x) \]
**9. Problem 5.3.1.19:**
\[ xy'' + 3y' + x^3y = 0 \]
These problems involve finding general solutions to differential equations. In problem 8, use the substitution \( y = \sqrt{x}u(x) \) to simplify the problem.
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