Existence uniqueness wronskian

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SUMMARY

The discussion centers on solving the differential equation y'' - 4y = 12x. Participants reference "Theorem 3.1.1" as potentially relevant to the solution process, although its specific content is not detailed. There is uncertainty regarding the constant c, particularly the choice of c = -3, which was suggested by Wolfram Alpha but lacks clear justification in the context of the problem. Overall, the conversation highlights the need for clarity in applying theorems and constants in differential equations.

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  • Understanding of second-order differential equations
  • Familiarity with the Wronskian determinant
  • Basic knowledge of theorems related to differential equations
  • Experience using computational tools like Wolfram Alpha
NEXT STEPS
  • Study the application of the Wronskian in determining the existence and uniqueness of solutions
  • Review "Theorem 3.1.1" in the context of differential equations
  • Practice solving second-order linear differential equations with non-homogeneous terms
  • Explore the use of Wolfram Alpha for verifying solutions to differential equations
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Students studying differential equations, mathematics educators, and anyone seeking to improve their problem-solving skills in applied mathematics.

bl4ke360
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Homework Statement



y''-4y=12x

Homework Equations



I don't know

The Attempt at a Solution



http://imageshack.us/a/img7/944/20130207102820.jpg

I'm not sure if I did this right, I'm putting this here to make sure. Please respond within 3 hours if you can because it will be due.
 
Last edited by a moderator:
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bl4ke360 said:

Homework Equations



I don't know

Really? I would have thought this "Theorem 3.1.1" would be relevant.

The rest of the answers seem fine.
 


Karnage1993 said:
Really? I would have thought this "Theorem 3.1.1" would be relevant.

The rest of the answers seem fine.

Well theorem 3.1.1 is a paragraph long, and not really an equation either. I'm not sure about letting c=-3 though, the only reason I did is because wolfram had it as part of the answer but I don't see how.
 

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