GATE Engineering Mathematics: Differential Equations: Classification of PDEs, wave, Laplace and heat equations by separation of variables – Previous Year Questions

5 GATE previous year questions on Differential Equations: Classification of PDEs, wave, Laplace and heat equations by separation of variables (Engineering Mathematics, Aerospace Engineering) with answers and explanations, from every paper.

1. GATE 2021 AE Q12 (1 mark, Multiple choice) – The partial differential equation u xx-4u xy+6u yy=x+2y is
2. GATE 2022 AE Q38 (2 marks, Multiple choice) – For f xx+f yy=0 and real separated solution f=a(x)b(y), which statement can be true?
3. GATE 2023 AE Q13 (1 mark, Multiple choice) – For u t+u x=0, -<x<, t0, and u(x,0)=e-x2, the solution at t=1 is
4. GATE 2026 AE Q13 (1 mark, Multiple choice) – The following equation with respect to (x, t), where a is a non-zero constant, represents . t + a x = 0
5. GATE 2025 AE Q14 (1 mark, Multiple choice) – The partial differential equation 2 u x2 + 42 u x y + 22 u y2 = 0 is .