JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q71

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MathematicsSingle correct+4 / -1Question 71 of 90

If $2x=y^{1/5}+y^{-1/5}$ and $(x^2-1)\dfrac{d^2y}{dx^2}+\lambda x\dfrac{dy}{dx}+ky=0$ , then λ + k is equal to :

−23

−24

−26

Answer and worked solution

Official answer: B

$y^{1/5}+y^{-1/5}=2x$ gives $y^{1/5}=x\pm\sqrt{x^2-1}$ , so $y=(x\pm\sqrt{x^2-1})^5$ , which satisfies
$(x^2-1)y''+xy'-25y=0.$
So λ = 1, k = −25 and λ + k = −24.

Topics:Higher-order derivatives

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 71