If f^ (x)=f(x)+ _ 0 ^ 2 f(t) d t, f(0)= 4-e^ 2 3 , then function f(x) is
Mathematics · JEE Main · NTA Exams — Differential Equations
If \(f^{\prime}(x)=f(x)+\int_{0}^{2} f(t) d t, f(0)=\frac{4-e^{2}}{3}\), then function \(f(x)\) is
- \(e^{x}-\frac{e^{2}-1}{3}\)
- \(2 e^{x}-\frac{e^{2}+2}{3}\)
- \(\frac{e^{x}}{3}-\frac{e^{2}-5}{3}\)
- None of these
Answer
(A) e^ x - e^ 2 -1 3
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