GATE 2023 ES – Question 47

Mathematics Foundation · Calculus · 2 marks · Numerical answer

Solve $y^{\prime\prime}-y^{\prime}-2y=0$ with y(0)=2,y′(0)=1 and find y(1),to three decimals.

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Show answer and explanation

Correct answer: 7.700 to 7.800

Explanation

Characteristic roots satisfy $(r-2)(r+1)=0$,so $y=Ae^{2x}+Be^{-x}$. Initial equations are A+B=2 and 2A−B=1,giving A=B=1. Therefore $y(1)=e^2+e^{-1}=7.7569355$,rounded **7.757**.

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