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GATE 2026 Chemical Engineering, Q62 · Mathematics

The correct answer is 2.24 to 2.26.

Question

Consider the differential equation x2(d2y/dx2)+x²(d²y/dx²) + 3x(dy/dx) − 3y = 0, with y = 3 and dy/dx = −5 at x = 1. The value of y at x = 2 is ______ (rounded off to two decimal places).

Official answer: 2.24 to 2.26

Why

GATE 2026 official key: 2.24 to 2.26. Trial y=xmy=x^{m} gives m2+2m−3=0,m²+2m−3=0, so m=1,−3: y=C1x+C2x−3.y=C1x+C2x⁻³. Using the initial conditions, C1=1, C2=2, so y(2) = 2 + 2/8 = 2.25.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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