GATE Ordinary Differential Equations: Laplace Transforms – Previous Year Questions

3 GATE previous year questions on Laplace Transforms (Ordinary Differential Equations, Mathematics) with answers and explanations, from every paper.

1. GATE 2021 MA Q39 (2 marks, Multiple choice) – For y″+ay′+by=f(t),a,b>0,a≠b,a²−4b=0, with y(0)=y′(0)=0, which Laplace-transform solution holds?
2. GATE 2025 MA Q12 (1 mark, Multiple choice) – Let Y(s) be the Laplace transform of Bessel J₀(x), with transforms of J₀ and its first two derivatives assumed to exist. Which relation holds for s>0?
3. GATE 2026 MA Q40 (2 marks, Multiple choice) – Let δ be the unit impulse (zero away from its point and total integral 1). Solve 2y+y+2y=(x-5), y(0) = y′(0) = 0. Which y(10) is correct?