GATE Engineering Mathematics: Differential Equations – Previous Year Questions

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

1. GATE 2021 BM Q38 (2 marks, Multiple choice) – Solve y/ t+5 y/ x=0 with y(x,0)=sin x for all real x, and evaluate y at x=π,t=π/6.
2. GATE 2022 BM Q37 (2 marks, Multiple choice) – Solve dy/dx−y=cos x, with c an arbitrary constant.
3. GATE 2023 BM Q36 (2 marks, Multiple choice) – A bacterial population satisfies dx/dt=x(1-x/200) with x(0)=100. What population is approached as t tends to infinity?
4. GATE 2024 BM Q37 (2 marks, Multiple choice) – Find a possible solution of / x=-2/ t and / x=-2/ t.
5. GATE 2025 BM Q39 (2 marks, Multiple choice) – y″−0.25y=0 with y(0)=1,y′(0)=1. Find y(ln100).
6. GATE 2026 BM Q61 (2 marks, Numerical answer) – Hormone concentration p in μg/dL obeys p(t)=e-0.1t-0.1p(t) for t≥0 hours, with p(0)=20. Find p(10), to one decimal place.