Differential Equation Power Series Method

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SUMMARY

The discussion centers on solving the differential equation (2x-1)y'+2y=0 using the power series method. The user initially arrived at the solution 2c/(1-2x) but confirmed that the correct answer is c/(1-2x), where c is an arbitrary constant. The radius of convergence for the series is correctly identified as 1/2. The conversation highlights the importance of recognizing the arbitrary nature of constants in differential equations.

PREREQUISITES
  • Understanding of differential equations, specifically first-order linear equations.
  • Familiarity with power series and their convergence properties.
  • Knowledge of arbitrary constants in mathematical solutions.
  • Basic skills in manipulating algebraic expressions and functions.
NEXT STEPS
  • Study the method of power series solutions for differential equations.
  • Learn about the concept of arbitrary constants in mathematical solutions.
  • Explore the implications of radius of convergence in power series.
  • Practice solving first-order linear differential equations using various methods.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on differential equations and power series methods, as well as anyone looking to deepen their understanding of solution techniques in this area.

lclauber
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Differential Equation Power Series Method (Almost done!)

Homework Statement


solve (2x-1)y'+2y=0 using power series.
I'm really close to the correct answer, which is c/(1-2x). I keep getting 2c/(1-2x).
I got the correct radius of convergence, however (1/2)

Homework Equations


shown in my attempt at a solution.

The Attempt at a Solution


attached as a png.
 

Attachments

  • diffeqproblem7.png
    diffeqproblem7.png
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Last edited:
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welcome to pf!

hi lclauberc welcome to pf! :smile:
lclauber said:
I'm really close to the correct answer, which is c/(1-2x). I keep getting 2c/(1-2x).

erm :redface: …

c is arbitrary! :wink:​
 
*facepalm* lol.
Thank you!
 

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