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GATE ME 2025 Set 1 — Question 47

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

Engineering Mathematics → Differential Equations → Euler-Cauchy Equation

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Question

Let yy be the solution of the differential equation with the initial conditions given below. If y(x=2)=Aln⁡2y(x = 2) = A \ln 2, then the value of AA is ____________ (rounded off to 2 decimal places).x2d2ydx2+3xdydx+y=0y(x=1)=0,dydx(x=1)=1x^2 \frac{d^2y}{dx^2} + 3x \frac{dy}{dx} + y = 0 \quad y(x = 1) = 0, \quad \frac{dy}{dx}(x = 1) = 1
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