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GATE 2024 MA – Question 63

Ordinary Differential Equations · Higher Order Equations and Systems · 2 marks · Numerical answer

The BVP x²y″−2xy′+2y=0 on [1,2], y(1)−y′(1)=1, y(2)−ky′(2)=4, has infinitely many solutions for which k? (two decimals)

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Correct answer: 1.99 to 2.01

Explanation

Euler roots are 1,2, so y=ax+bx². First boundary gives (a+b)−(a+2b)=−b=1, hence b=−1. Second becomes (2−k)a+(4−4k)b=4. For a arbitrary, require k=2; then the b term is (−4)(−1)=4, so the condition holds for every a. **2.00**.

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