GATE Engineering Mathematics: Differential Equations: Heat, wave and Laplace equations – Previous Year Questions

3 GATE previous year questions on Differential Equations: Heat, wave and Laplace equations (Engineering Mathematics, Mechanical Engineering) with answers and explanations, from every paper.

1. GATE 2022 ME (ME1) Q12 (1 mark, Multiple choice) – Solution of 2T = 0 in a square domain (0 < x < 1 and 0 < y < 1) with boundary conditions: T(x, 0) = x; T(0, y) = y; T(x, 1) = 1 + x; T(1, y) = 1 + y…
2. GATE 2025 ME Q12 (1 mark, Multiple choice) – For the differential equation given below, which one of the following options is correct? 2 u x2 + 2 u y2 = 0 0 x 1, 0 y 1
3. GATE 2026 ME Q37 (2 marks, Multiple choice) – Consider the following differential equation y x = 3 y t + y If y(x, 0) = 10e-2x, then the solution of the differential equation is