Cauchy Method/ UC set OR Variation of Param?

In summary, the conversation discusses the problem of getting two different answers when solving a differential equation using two different methods - Cauchy method and Variation of Parameters. The person is unsure which method is correct and mentions that the Undetermined Coefficients method cannot be used with certain functions. They also suggest using a substitution to turn the equation into one with constant coefficients. They ask for someone to show their work and the answer they got.
  • #1
dgutierrez079
1
0
Hello new to this forum , Was solving some Diff eq problems and iam getting two different answers using two methods, ok the problem is i=primes (x^2)(y^ii)+(x)(y^i)+y=4sin(lnx)
This is cauchy method, When i use variation of parameters i get a long answer with impossible integrals and when i use Undetermined coefficients i also get an answer, Not sure witch is correct i also understand that Uc method can't be used with tanx, secx, lnx, but in this case that there is a sin in there iam not sure. Thanks
 
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  • #2
Please show what you did and what answer you got.

(Note that the substution u= ln(x) turns this into the differential equation with constant coefficients, y''+ y= ln(u) where the primes now indicate differentiation with respect to u.)
 

1. What is the Cauchy method?

The Cauchy method is a mathematical technique used to solve a system of equations through iteration. It involves starting with an initial approximation and using this to improve the solution through multiple iterations until a desired level of accuracy is achieved.

2. What is the UC set in the context of Cauchy method?

The UC set, also known as the ultimate convergence set, is a set of values that the Cauchy method can converge to. It represents the set of all possible solutions to the system of equations being solved.

3. How is the Cauchy method related to the variation of parameters method?

The Cauchy method is a specific application of the more general variation of parameters method. While the Cauchy method is used to solve a system of equations, the variation of parameters method can be applied to solve a wider range of mathematical problems.

4. What are the advantages of using the Cauchy method over other methods of solving systems of equations?

The Cauchy method is a relatively simple and straightforward technique that can be easily implemented without the need for advanced mathematical knowledge. It also has the advantage of being able to provide a range of potential solutions rather than a single solution, allowing for greater flexibility in problem-solving.

5. What are the limitations of the Cauchy method?

One limitation of the Cauchy method is that it may not always converge to the desired solution, particularly if the initial approximation is not close enough to the actual solution. Additionally, the method may not be suitable for solving certain types of nonlinear systems of equations.

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