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GATE 2019 ME (ME2) – Question 37

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

Solve $x^2y^{\prime\prime}-2xy^\prime+2y=4$ in arbitrary constants $C_1,C_2$.

  1. $y=C_1x^2+C_2x+2$
  2. $y=C_1/x^2+C_2x+2$
  3. $y=C_1x^2+C_2x+4$
  4. $y=C_1/x^2+C_2x+4$

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Correct answer: (A) $y=C_1x^2+C_2x+2$

Explanation

For $y=x^m$, the homogeneous Euler equation gives $m(m-1)-2m+2=(m-1)(m-2)=0$. A constant particular solution is 2. Thus **$y=C_1x^2+C_2x+2$, A**.