Consider the ordinary differential equation x²(d²y/dx²) − x(dy/dx) − 3y = 0, with the boundary conditions y(x=1) = 2 and y(x=2) = 17/2. The solution y(x) at x = 3/2, rounded off to 2 decimal places, is ___________

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Accepted Answer

The correct answer is 4 to 4.08. GATE 2024 official key: 4.00 to 4.08. This Cauchy-Euler equation has solutions y=x^m with m²−2m−3=0 ⇒ m=3,−1, so y=C1x³+C2/x. BCs give C1=C2=1, so y(x)=x³+1/x. At x=1.5: y=3.375+0.667≈4.04.