GATE 2022 MA – Question 33

Ordinary Differential Equations · Series Solutions and Special Functions · 1 mark · Numerical answer

If x²φ″+xφ′+x²φ=0,x>0 has a Frobenius solution $\phi=x^r\sum_{n\ge0}a_nx^n$ with a₀≠0, find r²+1.

Show answer and explanation

Correct answer: 1 to 1

Explanation

The lowest power xʳ has coefficient [r(r−1)+r]a₀=r²a₀; the x²φ term starts two orders later. Therefore r²=0, and **r²+1=1**.

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