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GATE BT 2024 | Question: 20

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The solution of the differential equation $\frac{d y}{d x}=y+e^{-x}$ that satisfies $y(0)=-\frac{1}{2}$ is $\_\_\_\_\_\_\_$.

  1. $-\frac{1}{2} e^{-\frac{x}{2}}$
  2. $-\frac{1}{2} e^{x}$
  3. $-\frac{1}{2} e^{-x}$
  4. $-\frac{1}{2} e^{\frac{x}{2}}$

     

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