The GATE Grind

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

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

  1. GATE 2023 ME Q49 (2 marks, Numerical answer) – Consider the second-order linear ordinary differential equation x2d2ydx2 + xdydx - y = 0, x 1 with the initial conditions y(x = 1) = 6, dydx x=1 = 2.…
  2. GATE 2024 ME Q43 (2 marks, Numerical answer) – If x(t) satisfies the differential equation tdxdt + (t - x) = 0 subject to the condition x(1) = 0, then the value of x(2) is (*rounded off to 2…
  3. GATE 2025 ME Q47 (2 marks, Numerical answer) – Let y be the solution of the differential equation with the initial conditions given below. If y(x = 2) = A 2, then the value of A is (rounded off to…
  4. GATE 2026 ME Q13 (1 mark, Multiple choice) – The order and degree of the following differential equation are m and n, respectively. 3 x3 + 2 y2 x + (2 x2)2 + y = 0 The value of (m - n) is