What is wrong here? (A differential equation)

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SUMMARY

The discussion centers on a Sturm-Liouville eigenvalue problem defined by the differential equation Lu = u'' - u = 0 over the interval x ∈ (0,1) with boundary conditions u(0) = u(π) = 0. The only solution identified is u(x) = 0, which initially appears trivial. However, the participant later realizes the relevance of Fredholm's alternative in understanding the problem's implications, indicating a deeper insight into the nature of eigenvalue problems.

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  • Understanding of Sturm-Liouville theory
  • Familiarity with differential equations and boundary value problems
  • Knowledge of eigenvalue problems and eigenfunctions
  • Experience using computational tools like Wolfram Alpha for solving equations
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  • Study the implications of Fredholm's alternative in eigenvalue problems
  • Explore advanced Sturm-Liouville problems and their applications
  • Learn about the characteristic equation in the context of differential equations
  • Investigate numerical methods for solving boundary value problems
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Students and educators in mathematics, particularly those focusing on differential equations, eigenvalue problems, and Sturm-Liouville theory.

Jamin2112
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What is wrong here? (A differential equation)

Homework Statement



My homework has a Sturm-Louiville eigenvalue problem

Lu = u'' - u = 0, x ε (0,1)​

with u(0)=u(∏)=0. The only solution is u(x) = 0, x ε [0,1]. Right? But then other parts of this particular problem become trivial.

Homework Equations



Nothing really

The Attempt at a Solution



Plugged it into Wolfram Alpha to get u(x)=0, solved it using the characteristic equation to get u(x)=0, and also did the eigenfunction expansion to get the same answer.
 
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nevermind! I just saw fredholm's alternative in the lecture notes. I get it now.
 

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