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The functions $f(x)$ and $g(x)$ satisfy $f(0) = 3,$ $g(0) = -4,$ and \begin{align*} f'(x) &= 7f(x) + 2g(x), \\ g'(x) &= -4f(x) + g(x). \end{align*}Find $f(x).$
Jul 24, 2021