The GATE Grind

GATE 2022 IN – Question 45

Engineering Mathematics · Differential equations · 2 marks · Multiple choice

For $dy/dx+y\ln y=0$ with $y(0)=e$, the value of $y(1)$ is ______.

  1. $e^e$
  2. $e^{-e}$
  3. $e^{1/e}$
  4. $e^{-1/e}$

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Correct answer: (C) $e^{1/e}$

Explanation

Set u=ln y, so u′=y′/y=−u. Initial u(0)=1 gives u=e⁻ˣ and y=exp(e⁻ˣ). At x=1, **y=e^(1/e), C**.