Mathematics · Integral Equations
Consider the integral equation ∫0x (x - t)u(t)dt = x for x ≥ 0 for continuous functions u defined on [0, ∞). The equation has:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1More than one solution u such that |u(x)| ≤ C(1 + |x|) for some constant C
- 2A unique solution u such that |u(x)| ≤ C(1 + |x|) for some constant C✓
- 3No solution
- 4A unique bounded solution
Correct answer
A unique solution u such that |u(x)| ≤ C(1 + |x|) for some constant C
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