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A function y(x) satisfies y'(x) = y(x) + (integral from 0 to 1 of y dx) with y(0) = 1. Find the value of y at x = ln((11 - 3e)/2).
- 2
- 3
- 4
- 5
Correct answer: 4
Solution
Treating the definite integral as a constant k gives y = A e^x - k; using y(0)=1 and computing k from its own definition yields A = 2/(3-e), and substitution gives y = 4 at the stated x.
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