Consider the second-order linear ordinary differential equation x^{2} {d^{2}y}/{dx^{2}} + x\frac{dy}{dx}−y = 0,x \geq 1 with the initial conditions y(x = 1) = 6,\frac{dy}{dx} |._{x = 1} = 2 The value of 𝑦 at 𝑥 = 2 equals ________. (Answer in integer)

GATE Mechanical Engineering (ME) 2023 Shift 1 Solved Paper

Question : 49 of 65

Marks: +1, -0

Consider the second-order linear ordinary differential equation

x^{2}\;{d^{2}y}/{dx^{2}} + x\;{dy}/{dx}−y = 0,x ≥ 1

with the initial conditions

y(x = 1) = 6,\;{dy}/{dx} |._{x = 1} = 2

The value of 𝑦 at 𝑥 = 2 equals ________.
(Answer in integer)

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