GATE 2019 ME (ME1) – Question 13

Engineering Mathematics · Differential Equations: First order and higher order linear equations, Euler-Cauchy equation · 1 mark · Multiple choice

For $dy/dx+7x^2y=0$ with y(0) = 3/7, find y(1).

$\frac73e^{-7/3}$
$\frac73e^{-3/7}$
$\frac37e^{-7/3}$
$\frac37e^{-3/7}$

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Correct answer: (C) $\frac37e^{-7/3}$

Explanation

Separation gives $dy/y=-7x^2dx$, so $y=Ce^{-7x^3/3}$. The initial value gives C=3/7. Substituting x=1 yields **$(3/7)e^{-7/3}$, C**. The exponent contains x cubed because the coefficient is 7x squared.