GATE Ordinary Differential Equations: First Order Equations and Initial Value Problems – Previous Year Questions

3 GATE previous year questions on First Order Equations and Initial Value Problems (Ordinary Differential Equations, Mathematics) with answers and explanations, from every paper.

1. GATE 2022 MA Q19 (1 mark, Multiple choice) – For real y₀, the initial value problem y′=cos(xy),x∈ℝ,y(0)=y₀ has how many solutions?
2. GATE 2024 MA Q24 (1 mark, Multiple choice) – y₁,y₂ are different solutions of y+(ex)y=(ex+1) on [0,1]. Select the general solution, constants real.
3. GATE 2024 MA Q44 (2 marks, Multiple choice) – For y′=e(−y²)+1,y(0)=0, I:the IVP has a unique solution on ℝ. II:Every solution is bounded on its maximal existence interval. Choose truth values.