Please show me a solution to the differential equation

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Discussion Overview

The discussion revolves around the differential equation y''(x) - A x^2 y = 0, where A is a constant. Participants explore potential solutions and related concepts, including references to known functions and resources.

Discussion Character

  • Debate/contested, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant requests a solution to the differential equation, suggesting it may be straightforward.
  • Another participant expresses doubt about the simplicity of the equation and provides links to external resources that may contain solutions.
  • A third participant mentions the intention to work with Bessel functions in relation to the equation.
  • Another participant contests the idea that the solution involves Bessel functions, proposing instead that it resembles a Harmonic Oscillator and suggesting a solution involving a constant and exp(x^2).
  • This participant also clarifies that the form of the differential equation for Bessel functions differs from the one presented.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the solution, with some suggesting Bessel functions and others asserting it relates to Harmonic Oscillators. No consensus is reached regarding the solution.

Contextual Notes

There are unresolved assumptions regarding the nature of the solutions and the definitions of the functions involved. The discussion does not clarify the mathematical steps necessary to derive the proposed solutions.

edgepflow
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Can someone solve:

y''(x) - A x^2 y = 0

A = constant

It is probably easy, but I took this class 23 years ago.
 
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This one's not so easy as far as I can tell. Fortunately others have figured it out already: http://eqworld.ipmnet.ru/en/solutions/ode/ode0202.pdf

Here's a great website when you have an ODE that you think someone might have solved before: http://eqworld.ipmnet.ru/en/solutions/ode.htm

I referred to the book the authors of that website have written. They have some different things written about a more general form of this equation. This book might be worth tracking down if the link above doesn't help.
 
Last edited:
Thanks btrettel! I had a feeling that equation had an attitude.

Now I will grind out some Bessel functions.
 
Its solution is not Bessel Function. Its a Harmonic Oscillator.
its solution must be some constant with exp(x^2).
the differential equation for Bessel function is
x^2Y''+xY'+(x^2-n^2)y=0
which is of course not ur differential equation.
 

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