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GATE 2019 CE (CE2) – Question 38

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

Solve $(x\ln x)\frac{dy}{dx}=y$, with K a constant.

  1. $y=Kx\ln x$
  2. $y=Kxe^x$
  3. $y=Kxe^{-x}$
  4. $y=K\ln x$

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Correct answer: (D) $y=K\ln x$

Explanation

Separate variables: $dy/y=dx/(x\ln x)$. Integrating gives $\ln|y|=\ln|\ln x|+C$. Hence **y = K ln x, D** on a suitable domain. Differentiation verifies the result; K = 0 includes the zero solution.