problem 8 just please using Bessel Functions **Problem 5.3.1.12:**\[ x^2 y'' + \left( \alpha x^2 - \nu^2 + \frac{1}{4} \right) y = 0, \text{ use } y = \sqrt{x} u(x) \] **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.

The given equation is x2y''+a2x2-v2+14y=0 The objective is to find the solution for the problem…

Answered: 8. Problem 5.3.1.12: x²y" + (a²x² – v²…

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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

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

problem 8 just please using Bessel Functions

**Problem 5.3.1.12:**

\[ x^2 y'' + \left( \alpha x^2 - \nu^2 + \frac{1}{4} \right) y = 0, \text{ use } y = \sqrt{x} u(x) \]

**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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