GATE Engineering Mathematics: Differential Equations – Previous Year Questions

8 GATE previous year questions on Differential Equations (Engineering Mathematics, Production and Industrial Engineering) with answers and explanations, from every paper.

1. GATE 2022 PI Q24 (1 mark, Numerical answer) – Find the order of (dy/dx)2+5\,dy/dx+4y=5x3 (integer).
2. GATE 2022 PI Q37 (2 marks, Multiple choice) – Find the general solution of 4y-4y+y=0, with arbitrary constants c₁,c₂.
3. GATE 2023 PI Q12 (1 mark, Multiple choice) – Which differential equation is nonlinear?
4. GATE 2024 PI Q46 (2 marks, Numerical answer) – x(t)+4x(t)=e-t for t ≥ 0, with x(0) = x′(0) = 0. Find x(π/8) to three decimals.
5. GATE 2025 PI Q13 (1 mark, Multiple choice) – If F(s) is the Laplace transform of f(t), find the transform of ebtf(t) for real constant b.
6. GATE 2025 PI Q14 (1 mark, Multiple choice) – Which differential equation is linear?
7. GATE 2025 PI Q36 (2 marks, Multiple choice) – Solve dy/dx+y=ex with y(0) = 0.
8. GATE 2026 PI Q60 (2 marks, Numerical answer) – dy/dt=2y and y(0) = 2. Find y(1), rounded to two decimals.