GATE 2021 ES – Question 52
Function y satisfies $y^{\prime\prime}-y^{\prime}=0$,y→1 as x→−∞,and y(0)=2. Find $y^{\prime}(0)$ as an integer.
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Show answer and explanation
Correct answer: 1 to 1
Explanation
The characteristic roots are0 and 1,so y=A+Beˣ. As x→−∞,eˣ→0,forcing A=1. Then y(0)=1+B=2 gives B=1. Differentiation gives y′=eˣ and therefore **y′(0)=1**.