Need Help with an Asymptotic Solution for a Differential Equation

  • Thread starter Thread starter anton
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on finding an asymptotic solution for the differential equation 3/2y(x) + xy'(x) + y'''(x) = 0 as x approaches infinity. Participants reference two significant works: Hershenov's 1976 paper on a related differential equation and Pfeiffer's 1972 study on asymptotic solutions. The user expresses difficulty in accessing these articles and seeks guidance on the asymptotic behavior of the equation y''' - 4xy' - 2y = 0, which is identified as a generalized Airy's equation. The conversation highlights the need for accessible resources and expert advice on this specific mathematical problem.

PREREQUISITES
  • Understanding of differential equations, particularly third-order equations.
  • Familiarity with asymptotic analysis techniques.
  • Knowledge of generalized Airy equations and their properties.
  • Ability to access and interpret academic papers in mathematics.
NEXT STEPS
  • Research Hershenov's 1976 paper on solutions of the differential equation y''' + axy' + by = 0.
  • Investigate Pfeiffer's 1972 work on asymptotic solutions of y''' + q(x)y' + r(x)y = 0.
  • Study the properties and solutions of generalized Airy equations.
  • Explore online databases or libraries for accessing mathematical journals and articles.
USEFUL FOR

Mathematicians, students of differential equations, and researchers seeking to understand asymptotic solutions and their applications in advanced mathematics.

anton
Messages
7
Reaction score
0
Hi community :P

Need some help with a differential Equation:

3/2y(x)+xy'(x)+y'''(x)=0

actually I'm looking for an asymptotic solution, when x -> infinity.

I made some research about that Eq. and here what i have found:

1 guy found an asymptotic sol. for a more general eq.:

Hershenov, J. Solutions of the differential equation y''' +axy'+by = 0. Stud. Appl. Math. 55 (1976), 301-314.

other guy found a solution of a more general eq:

Pfeiffer, G. W. Asymptotic solutions of y"'+q(x)y'+r(x)y=0. J. Differential Equations 11 (1972), 145-155.

but unfortunaly i can't find any of those articles.

and the last thing which i know:

the eq. y'''-4xy'-2y=0 is a generaliaed Airy's eq. whose solutions are well studied...but its not a thing I am looking for...

any advice is very appreciated.
and if some one could find one of those articles i'll appreciate that VERY MUCH!

Thx for your concideration.

PS: Sorry my bad english.
 
Physics news on Phys.org
sry... mistake with the right forum for the thread.
Move it please to Diff. Eq. forum.
thx
 

Similar threads

Solve these two coupled first-order differential equations and sketch the flow
  • · Replies 2 ·
Replies
2
Views
2K
The Harmonic Oscillator Asymptotic solution?
  • · Replies 21 ·
Replies
21
Views
3K
Help understanding modal projection in PDE with assumed solution form
  • · Replies 4 ·
Replies
4
Views
1K
Help with a calculation about gravitational waves
  • · Replies 1 ·
Replies
1
Views
2K
Series solution for differential equation
  • · Replies 2 ·
Replies
2
Views
2K
Understanding solution to equations of motion of n coupled oscillators
  • · Replies 4 ·
Replies
4
Views
2K
Fourier transform of the Helmholtz equation
  • · Replies 4 ·
Replies
4
Views
4K
Find the equation knowing its asymptote in the infinite
  • · Replies 1 ·
Replies
1
Views
868
Current through Ballistic 2DEG Channel
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
1K