II order homogeneous differential equation solution

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SUMMARY

The discussion focuses on solving the second-order homogeneous differential equation given by a\frac{d^{2}x}{dr^{2}} + (br + c/r)\frac{dx}{dr} + dx = 0, which arises in the context of damped harmonic oscillation. The user specifically notes that the Frobenius method is not applicable for this equation. Participants in the forum are encouraged to explore alternative methods for finding solutions to this type of differential equation.

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Sourabh N
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I am trying to solve the diff. equation -

a[tex]\frac{d^{2}x}{dr^{2}}[/tex] + (br + c/r)[tex]\frac{dx}{dr}[/tex] + dx = 0

I got it while solving a variant of damped harmonic oscillation.

Any hints (Frobenius method won't work)
 
Last edited:
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a[tex]\frac{d^{2}x}{dr^{2}}[/tex] + (br + c/r)[tex]\frac{dx}{dr}[/tex] + dx = 0

Sorry, this is the correct eqn.
 
Last edited:

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