How to solve Differential equation

Click For Summary

Discussion Overview

The discussion revolves around solving a specific differential equation of the form \( y'' + a\frac {y} {x} + b\frac {y} {x^2} = 0 \). Participants explore various methods and transformations related to this equation, including the use of series solutions and connections to modified Bessel functions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about solving the differential equation.
  • Another participant mentions "Malmstén," suggesting a reference to a specific method or solution.
  • A proposed solution involves a power series approach, specifically a Frobenius series.
  • Some participants argue that Malmstén's solution in terms of modified Bessel functions is superior.
  • There is a suggestion to transform the equation to resemble the modified Bessel equation.
  • References to transformations found in Watson's book are made, indicating a specific resource for the transformations needed.
  • One participant expresses that they have found the solution after initially asking for help.

Areas of Agreement / Disagreement

Participants express differing views on the best method to solve the equation, with some favoring series solutions and others advocating for the use of modified Bessel functions. The discussion does not reach a consensus on the preferred approach.

Contextual Notes

The discussion includes references to specific transformations and resources, which may imply limitations based on the assumptions or definitions used in the proposed methods. The exact nature of the transformations and their implications for the solution remain unresolved.

giorgio_29
Messages
5
Reaction score
0
Hello!
How to solve this diff eq?

[tex]\ y'' + a[/tex][tex]\frac {y} {x}[/tex] [tex]\ +b[/tex][tex]\frac {y} {x^2}[/tex] [tex]\ = 0[/tex]
 
Physics news on Phys.org
Malmstén?
 
ANSAT:

[tex]y(x)=\sum_{n=0}^\infty a_n x^n[/tex]
 
yes Frobenius series for fuchsian points..., but Malmstén found the solution in term of modified Bessel functions, it is quite better.
 
Then you need to transform such equation to look like the modified Bessel equation.
 
yes yes

the transformations are in the Watson book

the equation transform into a Bessel equation by using Malmstén transformations.
 
Then what is the question?
 
after asking how to solve that equation I found the solution.

tks

gio
 

Similar threads

Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Solving Differential Equation Using Reduction of Order
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Question about the general solution to Hooke's law
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Partial Differential Equation solved using Products
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Expressing a differential equation into a different format
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Differential equation with two terms
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Can I Differentiate Both Sides to Solve y in y^2=ln(1-y^2)?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad General solution vs particular solution
  • · Replies 52 ·
2
Replies
52
Views
9K
Undergrad Integral-form change of variable in differential equation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate FEM basis polynomial order and the differential equation order
  • · Replies 1 ·
Replies
1
Views
3K