For t>0, solve y+2y+y=0 with y(0)=0 and y′(0)=1. Here u(t) is the unit step.

GATE 2016 EE (EE2) – Question 18

For t>0, solve $y^{\prime\prime}+2y\prime+y=0$ with y(0)=0 and y′(0)=1. Here u(t) is the unit step.

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Correct answer: (A) $te^{-t}u(t)$

The characteristic equation is (r+1)²=0, so $y(t)=(C_1+C_2t)e^{-t}$. From y(0)=0, C1=0.

Differentiate: y′(0)=C2−C1=1, giving C2=1. The causal expression is therefore **$te^{-t}u(t)$, A**.

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