The GATE Grind

GATE Engineering Mathematics: Differential Equations – Previous Year Questions

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

  1. GATE 2021 AG Q36 (2 marks, Multiple choice) – Solve y+y+.25y=0,y(0)=3,y(0)=-3.5.
  2. GATE 2023 AG Q14 (1 mark, Multiple choice) – y=aemx+be-mx solves which ODE?
  3. GATE 2024 AG Q12 (1 mark, Multiple choice) – Find the Laplace transform of f(t)=t4.
  4. GATE 2024 AG Q37 (2 marks, Multiple choice) – Solve y+2y-3y=0 with y(0)=0,y(0)=8.
  5. GATE 2025 AG Q13 (1 mark, Multiple choice) – s/(s2+a2) is the Laplace transform of which function of t?
  6. GATE 2025 AG Q14 (1 mark, Multiple choice) – Classify y+p(x)y+q(x)y=r(x).
  7. GATE 2025 AG Q43 (2 marks, Numerical answer) – Solve dy/dx=3y+2ex with y(0)=0 and find y at x=.3,to three decimals.
  8. GATE 2026 AG Q11 (1 mark, Multiple choice) – Identify these PDEs in order, where c is constant:(i) 2u 1 t2=c22u 1 x2,(ii) u 1 t=c22u 1 x2,(iii) 2u 2 x2+2u 2 y2=0.
  9. GATE 2026 AG Q13 (1 mark, Multiple choice) – Find the general solution of d2y/dx2= 2x.