GATE ME 2023 Set 1 — Question 49

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NAT+2 / -0MediumEuler-Cauchy EquationDifferential EquationsEngineering Mathematics

Engineering Mathematics → Differential Equations → Euler-Cauchy Equation

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Question

Consider the second-order linear ordinary differential equationx2d2ydx2+xdydxy=0,x1x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - y = 0, x \geq 1with the initial conditionsy(x=1)=6,dydxx=1=2.y(x = 1) = 6, \quad \left. \frac{dy}{dx} \right|_{x=1} = 2.The value of yy at x=2x = 2 equals _________.
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