Mathematics · Integral Equations
For the unknown function y : [0, 1] → ℜ, consider the following two-point boundary value problem: y''(x) + 2y(x) = 0 for x ∈ (0,1), with boundary conditions y(0) = y(1) = 0. It is given that the above boundary value problem corresponds to the following integral equation: y(x) = 210K(x, t) y(t) dt for x ∈ [0, 1]. Which of the following is the kernel K(x, t)?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1K(x, t) = t(1 - x) for t x✓
- 2K(x, t) = t2(1 - x) for t x
- 3K(x, t) = √t(1 - x) for t x
- 4K(x, t) = √t3(1 - x) for t x
Correct answer
K(x, t) = t(1 - x) for t x
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