GATE 2025 MA – Question 28

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

Legendre P_n satisfies (1−x²)y″−2xy′+n(n+1)y=0, with P_n(1)=1. Find P₁₁′(1) (integer).

Show answer and explanation

Correct answer: 66 to 66

Explanation

Evaluate the polynomial equation at x=1. The y″ term vanishes, giving −2P_n′(1)+n(n+1)=0. Thus P₁₁′(1)=11×12/2=**66**.

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