Find the general solution of x2y+xy-y=0 for x≠0.

GATE 2020 PI – Question 36

Engineering Mathematics · Differential Equations · 2 marks · Multiple choice

Find the general solution of $x^2y\prime\prime+xy\prime-y=0$ for x≠0.

$C_1/x+C_2/x^3$
$C_1x^2+C_2/x^2$
$C_1x+C_2/x$
$C_1x+C_2x^3$

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Correct answer: (C) $C_1x+C_2/x$

Explanation

For this Euler equation try y=xᵐ. Substitution gives m(m−1)+m−1=m²−1=0, so m=±1. The independent solutions are x and1/x, giving C on an interval excluding zero.

GATE 2020 PI – Question 36

Explanation

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