Mathematics · Integral Equations
For the Fredholm integral equation: y(s) = λ ∫ 0 1 e s e t y(t) dt Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1It has non-trivial solutions only if λ = 2 e 2 - 1 and ∫ 0 1 e t y(t) dt ≠ 0✓
- 2It has a non-trivial solution for all λ ≠ 0
- 3Only the trivial solution satisfies ∫ 0 1 e t y(t) dt = 0
- 4It has a non-trivial solution satisfying ∫ 0 1 e t y(t) dt = 0
Correct answer
It has non-trivial solutions only if λ = 2 e 2 - 1 and ∫ 0 1 e t y(t) dt ≠ 0
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