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GATE 2014 EE (EE2) – Question 15

Engineering Mathematics · Differential Equations: First order equations, Higher order linear differential equations, Variation of parameters, Cauchy and Euler equations, Partial differential equations, Separation of variables · 1 mark · Multiple choice

Which solves $x^2y^{\prime\prime}+xy^\prime-y=0$ for x > 0?

  1. $e^x$
  2. $x^2$
  3. $1/x$
  4. $\ln x$

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Correct answer: (C) $1/x$

Explanation

Try y=x^m. Substitution gives[m(m−1)+m−1]x^m=(m²−1)x^m=0,so m=±1. The general solution is Ax+B/x for x>0. Among the choices **1/x,C** is a solution; ln x would give−ln x rather than zero.