A function \( f \) satisfies the condition \( f(x)=f^{\prime}(x)+f^{\prime \prime}(x) \) \( +f^{...

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A function \( f \) satisfies the condition \( f(x)=f^{\prime}(x)+f^{\prime \prime}(x) \) \( +f^{\prime \prime}(x)+\ldots \), where \( f(x) \) is a differentiable function
\( \mathrm{P} \) indefinitely and dash denotes the order of derivative. If

W \( f(0)=1 \), then \( f(x) \) is
(1) \( e^{x / 2} \)
(2) \( e^{x} \)
(3) \( e^{2 x} \)
(4) \( e^{4 x} \)
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