2nd Order Linear ODE w/ nonconstant coefficient

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SUMMARY

The discussion focuses on solving the second-order linear ordinary differential equation (ODE) given by xy'' + 2xy' - y = 0. Participants highlight the complexity of the solution, referencing Wolfram Alpha for a compact answer that utilizes the substitution e^(2x). The Frobenius method is identified as a suitable technique for tackling such equations, particularly in graduate-level mathematics for physicists courses.

PREREQUISITES
  • Understanding of second-order linear ordinary differential equations
  • Familiarity with the Frobenius method for solving ODEs
  • Basic knowledge of differential calculus
  • Experience with mathematical software like Wolfram Alpha
NEXT STEPS
  • Study the Frobenius method in detail for solving ODEs
  • Learn about substitutions in differential equations, specifically e^(2x)
  • Explore advanced techniques for solving nonconstant coefficient ODEs
  • Practice solving various second-order linear ODEs using different methods
USEFUL FOR

Mathematics students, physicists, and anyone interested in advanced techniques for solving ordinary differential equations, particularly those with nonconstant coefficients.

Valour549
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The answer in wolfram alpha is written in a compact form using the substitution e^2x. If the left hand side of the equation is solved implicitly you should get a answer to that portion of their answer that will look similar to the equation that you started with
 

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