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GATE 2017 ME (ME2) – Question 37

Engineering Mathematics · Differential Equations: First order and higher order linear equations, Euler-Cauchy equation · 2 marks · Numerical answer

For $3y^{\prime\prime}+27y=0$, $y(0)=0$, $y\prime(0)=2000$, the value of y at x = 1 is ______.

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Correct answer: 93 to 95

Explanation

Dividing by3 gives y-double-prime+9y=0, with general solution A cos(3x)+B sin(3x). The first initial condition sets A=0; differentiating and applying the second gives3B=2000. Thus y(1)=(2000/3)sin3=**94.08** with3 measured in radians.