GATE Partial Differential Equations: First Order Equations – Previous Year Questions

5 GATE previous year questions on First Order Equations (Partial Differential Equations, Mathematics) with answers and explanations, from every paper.

1. GATE 2021 MA Q16 (1 mark, Multiple choice) – For differentiable f:ℝ→ℝ, u(x,y)=xy+f(x²−y²) satisfies which equation?
2. GATE 2021 MA Q38 (2 marks, Multiple choice) – Solve xu x+u y=1 with u(x,0)=−x²,x>0. Find u(2,1).
3. GATE 2022 MA Q62 (2 marks, Numerical answer) – For xu x+(x²+y)u y=u on ℝ², u(2,y)=y−4. Find u(1,2).
4. GATE 2023 MA Q39 (2 marks, Multiple choice) – For xu x+yu y=u with data u(t,t)=f(t),t>0, consider: P:if f(t)=2t+1 there is a unique local solution near the initial curve. Q:if f(t)=2t−1 there are…
5. GATE 2025 MA Q51 (2 marks, Multiple select) – On ℝ,t>0, u t+3u x=u and v t+3v x=v², both with initial data cosx. Which statements hold?