Solving ODEs with Frobenius Method: Troubleshooting and Tips

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SUMMARY

The discussion focuses on troubleshooting the Frobenius method for solving ordinary differential equations (ODEs). The user encountered difficulties when multiplying sine and cosine functions with the solution terms y, y', and y". They also faced challenges in equating series for the second ODE and had issues with the coefficient a1 in the third ODE. The suggestion to express sine and cosine as Taylor series was provided to facilitate the solution process.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with the Frobenius method for series solutions
  • Knowledge of Taylor series expansions for sine and cosine functions
  • Basic skills in manipulating power series
NEXT STEPS
  • Study the Frobenius method in detail, focusing on its application to ODEs
  • Learn how to derive Taylor series for sine and cosine functions
  • Practice solving ODEs using series solutions with various initial conditions
  • Explore common pitfalls in series solutions and how to troubleshoot them
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Students and researchers in mathematics, particularly those studying differential equations, as well as educators teaching the Frobenius method and series solutions.

edgar
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i need your help...i had to solve some ode using the frobenius method but half-way through i stuck...
for the first ode
i didn't know what to do when i had to multiply the sinx and cosx with y,y',y"
ii)i had a problem because of the cosx and i couldn't equate the series...--->second ode
iii)a) the third is to be solved using frobenius, but a1 has a problem...,
b) by using y(x)=w(x)/x, i had to find the new solution
oh and x0=0
the ode formulas are attached...forgive me i am not a native english speaker and it is the first time i write in this kind of forum...also please help me as much as you can...i have a deadline until tommorow...thanks again...
 

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Since you are writing y as a Taylor's series, do the same with sine and cosine.
 

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