GATE 2021 MA – Question 60

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

A power-series solution y=Σₖ₌₀∞a_kxᵏ,a₀≠0, satisfies y″−24x²y=0. Find a₄/a₀.

Show answer and explanation

Correct answer: 2 to 2

Explanation

Compare the coefficient of x². The second derivative contributes 4×3a₄, and 24x²y contributes 24a₀. Thus 12a₄=24a₀ and **a₄/a₀=2**.

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