The GATE Grind

GATE Engineering Mathematics: Differential Equations: First order and higher order equations, Cauchy-Euler equations – Previous Year Questions

4 GATE previous year questions on Differential Equations: First order and higher order equations, Cauchy-Euler equations (Engineering Mathematics, Chemical Engineering) with answers and explanations, from every paper.

  1. GATE 2023 CH Q31 (1 mark, Numerical answer) – The position x(t) of a particle, at constant , is described by the equation d2xdt2 = -2x. The initial conditions are x(t = 0) = 1 and .dxdt t=0 = 0.…
  2. GATE 2024 CH Q52 (2 marks, Numerical answer) – Consider the ordinary differential equation x2d2ydx2 - xdydx - 3y = 0, with the boundary conditions y(x = 1) = 2 and y(x = 2) = 17/2. The solution…
  3. GATE 2025 CH Q44 (2 marks, Multiple select) – Consider the differential equation dydx + yx = 0 Choose the CORRECT option(s) for the solution y.
  4. GATE 2026 CH Q62 (2 marks, Numerical answer) – Consider a differential equation: x2d2ydx2 + 3xdydx - 3y = 0 y = 3, dydx = -5 at x = 1 The value of y at x = 2 is (rounded off to two decimal places).