General Solution from Particular Solution

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SUMMARY

The discussion centers on finding the general solution of a second-order differential equation given two particular solutions, y1 and y2. Participants suggest using the method of variation of parameters as a viable approach. Additionally, Abel's theorem is mentioned as a technique to incorporate constants from one solution into the general solution. Both methods are established techniques in solving differential equations.

PREREQUISITES
  • Understanding of second-order differential equations
  • Familiarity with the method of variation of parameters
  • Knowledge of Abel's theorem
  • Basic concepts of particular and general solutions in differential equations
NEXT STEPS
  • Research the method of variation of parameters in detail
  • Study Abel's theorem and its applications in differential equations
  • Explore examples of deriving general solutions from particular solutions
  • Learn about other methods for solving second-order differential equations
USEFUL FOR

Students, mathematicians, and engineers who are studying differential equations and seeking to deepen their understanding of solution techniques.

Just_some_guy
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Just a question about the theory of solutions to differential equations?

Given a second order differential equation and two particular solutions y1 and y2, what is the best way to find the general solution?

i.e variation of parameters or something else
 
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Or perhaps to use one solution and contain all constants using Abel's theorem?
 

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