Solve a second-order differential equation

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Discussion Overview

The discussion revolves around solving a second-order differential equation, with participants examining a specific solution and its components. The focus includes identifying potential typos and clarifying terms within the solution.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant mentions a provided solution, referencing it as "(24)" without further details.
  • Another participant expresses a desire to understand the method for solving the differential equation.
  • Concerns are raised about a potential typo in the equation, specifically questioning whether "x" should be "y" in the term ##-{1\over a } {d\Psi(y)\over dx }##.
  • There is a query about the meaning of the subscript "1" in the term ##e_1^{-\sqrt B y}##.
  • One participant speculates that the solution may involve a form like ##y^p e^q## and suggests that additional components may have been grouped into an ##F_1## function with three arguments.
  • A later reply confirms the suspicion of a typo, reiterating that it should be "y" instead of "x".
  • Another participant asks for clarification on the origin of the equation and its implications.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the notation and components of the solution, with some agreeing on the presence of a typo while others seek further clarification on the overall context and meaning of the equation. The discussion remains unresolved with multiple viewpoints presented.

Contextual Notes

There are indications of missing assumptions regarding the definitions of terms and the context of the differential equation, as well as unresolved questions about the implications of the proposed solution.

Sara_76
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TL;DR
Can I find help in solving this equation
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Hello sara, ##\qquad## :welcome: ##\qquad## !

The solution is given: (24)
 
welcome

I want to know how to solve
 
The more I look at it, the stranger the whole thing seems to be.
##-{1\over a } {d\Psi(y)\over dx }\ ## -- a typo (##x## should be ##y##) ?
and (in 24) ##\ \ \ e_1^{-\sqrt B y} \ ## -- what is the subscipt 1 ?

Looks as if they tried ## y^p e^q## and swept the leftovers in an ##F_1## (with three arguments ?) ...
 
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for −1/adΨ(y)/dx
It's a mistake in writing (It's y, not x )
 
Where does this come from and what is it leading to ?
 

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