GATE 2025 PI – Question 36
Engineering Mathematics · Differential Equations · 2 marks · Multiple choice
Solve $dy/dx+y=e^x$ with y(0) = 0.
- $y=(e^x-e^{-x})/2$
- $y=(e^x+e^{-x})/2$
- $y=e^x-e^{-x}$
- $y=e^x+e^{-x}$
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Show answer and explanation
Correct answer: (A) $y=(e^x-e^{-x})/2$
Explanation
The integrating factor is $e^x$, giving $(ye^x)^\prime=e^{2x}$. Integrating yields $y=e^x/2+Ce^{-x}$. Initial value zero gives C = −1/2, so **A**.
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