GATE 2016 EE (EE2) – Question 40

The function y solves $y^{\prime\prime}-4y\prime+4y=0$ with y(0)=0 and y′(0)=1. The value y(1) is ________.

Show answer and explanation

Correct answer: 7.0 to 7.5

Explanation

The characteristic polynomial is (r−2)², so y=(C1+C2x)e²ˣ. The first initial condition gives C1=0; differentiation at zero gives C2=1.

Thus y(x)=xe²ˣ and **y(1)=e²≈7.38906**, within the official 7.0–7.5 interval.

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