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The solution of the ordinary differential equation

$\frac{dy}{dx}+3y=1$, subjects to the initial condition $y=1$ at $x=0$, is

  1. $\frac{1}{3}\left ( 1+2e^{-x/3} \right )$
  2. $\frac{1}{3}\left ( 5-2e^{-x/3} \right )$
  3. $\frac{1}{3}\left ( 5-2e^{-3x} \right )$
  4. $\frac{1}{3}\left ( 1+2e^{-3x} \right )$
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