Find the power series in x-xo?

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SUMMARY

The discussion centers on finding the power series for the general solution of the differential equation y'' - y = 0, specifically at the point x0 = 3. Participants emphasize the importance of clearly typing out solutions instead of uploading files, as this aligns with the Problem Forum (PF) standards for effective assistance. The power series expansion is crucial for solving differential equations and understanding the behavior of solutions near specific points.

PREREQUISITES
  • Understanding of differential equations, specifically second-order linear equations.
  • Familiarity with power series and their convergence properties.
  • Knowledge of Taylor series expansions centered at specific points.
  • Basic skills in mathematical notation and problem-solving communication.
NEXT STEPS
  • Study the method of solving second-order linear differential equations.
  • Learn about Taylor series and their applications in approximating functions.
  • Research the convergence criteria for power series.
  • Explore the use of symbolic computation tools like Wolfram Alpha for solving differential equations.
USEFUL FOR

Students studying differential equations, mathematics educators, and anyone interested in mastering power series expansions in the context of solving differential equations.

Math10
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Homework Statement


Find the power series in x-x0 for the general solution of y"-y=0; x0=3.

Homework Equations


None.

The Attempt at a Solution


I'll post my work by uploading it.
 
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This is my work.
 

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And the answer is
 

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Math10 said:

Homework Statement


Find the power series in x-x0 for the general solution of y"-y=0; x0=3.

Homework Equations


None.

The Attempt at a Solution


I'll post my work by uploading it.

Don't bother; most helpers will not read it. If you want help the safest way is to type out the solution, which is the PF standard, anyway.
 

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