GATE 2023 MA – Question 63

Ordinary Differential Equations · Series Solutions and Special Functions · 2 marks · Numerical answer

For 4(ln x)y″+3y′+y=0,x>1, let r₁,r₂ be the indicial roots at regular singular point x=1. Find |r₁−r₂| to two decimals.

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Correct answer: 0.24 to 0.26

Explanation

After division by 4 ln x, p=3/(4 ln x),q=1/(4 ln x). At x=1, p₀=lim(x−1)p=3/4 and q₀=lim(x−1)²q=0. The indicial equation is r(r−1)+(3/4)r=r(r−1/4)=0. Root difference **0.25**.

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