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GATE 2018 CE (CE1) – Question 48

Engineering Mathematics · ODE: First order and higher order linear equations, Euler-Cauchy equations, initial and boundary value problems · 2 marks · Numerical answer

For $y^{\prime\prime}+2y^\prime+y=0$, $y(0)=1$ and $y^\prime(0)=-1$, y at x = 1, to three decimals, is ______.

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Correct answer: 0.36 to 0.37

Explanation

The repeated characteristic root is −1, so $y=(C_1+C_2x)e^{-x}$. Initial value gives $C_1=1$, and initial derivative gives $C_2-C_1=-1$, hence $C_2=0$. Therefore $y(1)=e^{-1}=0.367879$, or 0.368.