How to solve a second order linear homeogeneous ODE with Frobenius?

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SUMMARY

The discussion focuses on solving a second-order linear homogeneous ordinary differential equation (ODE) using the Frobenius method, specifically the equation (X^2)(y'') - 6y = 0. The participant initially struggles due to the absence of a shift in the equation but later realizes that the indicial relations yield two values for the series solution. This highlights the importance of understanding series solutions in the context of differential equations.

PREREQUISITES
  • Understanding of second-order linear homogeneous differential equations
  • Frobenius method for solving differential equations
  • Concept of series solutions in differential equations
  • Knowledge of indicial relations in the context of power series
NEXT STEPS
  • Study the Frobenius method in detail, including examples without shifts
  • Explore series solutions to differential equations, focusing on convergence
  • Learn about recurrence relations in the context of power series
  • Investigate the application of indicial equations in solving ODEs
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Mathematics students, educators, and researchers interested in differential equations, particularly those focusing on series solutions and the Frobenius method.

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A simple question i think although i can't find in any books

What do u when u are solving a second order linear hoemoeneous differential equation with frobenius and there is no shift.

[tex](X^2)(y^{''}) (-6y)=0[/tex] it should be normal minus -6y

I only know what to do if there is a shift.Help someone?

This is otherwise known as series solutions to differential equations
 
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Does anybody know?

I keep trying but get nowhere i get an answer of 0 which i wrong.Help
 
Well i think i figured it out.
There is no recurrence relation and so your indical relations become your 2 values of the series.Thanks for the help.:rolleyes:
 

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