GATE 2025 AG – Question 43
Solve $dy/dx=3y+2e^x$ with $y(0)=0$ and find y at x=.3,to three decimals.
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Correct answer: 1.106 to 1.120
Explanation
Rearrange $y^{\prime}-3y=2e^x$ and multiply by integrating factor $e^{-3x}$. Then $(ye^{-3x})^{\prime}=2e^{-2x}$. Integrating gives $ye^{-3x}=-e^{-2x}+C$. Initial condition gives C=1,so $y=e^{3x}-e^x$. At .3,$y=e^{.9}-e^{.3}=1.109744\ldots$,rounded **1.110**.