- #1
Differential eqtn (What's wrong with my calculation?)
- Thread starter athrun200
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Homework Help Overview
The discussion revolves around a differential equation where the original poster is seeking clarification on their calculations, which differ from a textbook answer. The subject area is differential equations, specifically focusing on methods for solving equations with variable coefficients.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants discuss rewriting the differential equation and substituting trial solutions. There are inquiries about alternative methods for solving ordinary differential equations (ODEs) and the identification of the method being used. Some participants question the appropriateness of applying certain methods to equations with variable coefficients.
Discussion Status
The discussion is active, with participants providing different approaches and questioning the validity of methods used. Some guidance has been offered regarding the nature of the error in applying methods for constant coefficients to variable coefficient equations, but no consensus on a solution has been reached.
Contextual Notes
Participants are navigating the complexities of solving differential equations with variable coefficients, and there is a mention of a specific method related to Euler equations. The original poster's confusion stems from discrepancies between their calculations and established solutions.
- #2
vela
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Rewrite the differential equation slightly to get
[tex]\rho^2u''(\rho)-l(l+1)u(\rho) = 0[/tex]
Then substitute a trial solution of the form [itex]\rho^r[/itex] and then solve for r.
[tex]\rho^2u''(\rho)-l(l+1)u(\rho) = 0[/tex]
Then substitute a trial solution of the form [itex]\rho^r[/itex] and then solve for r.
- #3
athrun200
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vela said:
Is it another way to solve ODE?
What is the name of this method?
I can only remember to sub e^r
- #4
vela
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- #5
HallsofIvy
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You basic error is trying to apply a method that works for equations with constant coeficients to an equation with variable coefficients. As a result your characteristic equation, which should not involve the idependent variable, is wrong and everything after that is wrong.
- #6
- #7
Gib Z
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There is no simple answer for that one, though you can express it in terms of http://mathworld.wolfram.com/ParabolicCylinderFunction.html .
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