GATE Engineering Mathematics: Differential Equations – Previous Year Questions
14 GATE previous year questions on Differential Equations (Engineering Mathematics, Electronics and Communication Engineering) with answers and explanations, from every paper.
- GATE 2017 EC Q39 – Which one of the following is the general solution of the first order differential equation dydx = (x + y - 1)2, where x, y are real?
- GATE 2015 EC Q36 – The solution of the differential equation d2ydt2 + 2dydt + y = 0 with y(0) = y'(0) = 1 is
- GATE 2016 EC Q14 – Which one of the following is a property of the solutions to the Laplace equation: 2 f = 0?
- GATE 2018 EC Q44 – A curve passes through the point (x=1,\ y=0) and satisfies the differential equation dydx=x2+y22y+ yx. The equation that describes the curve is
- GATE 2018 EC Q60 – The position of a particle y(t) is described by the differential equation: d2ydt2=-dydt-5y4. The initial conditions are y(0)=1 and .dydt t=0=0. The…
- GATE 2019 EC Q12 – The families of curves represented by the solution of the equation dydx=-( xy)n for n=-1 and n=+1, respectively, are
- GATE 2019 EC Q53 – Consider the homogeneous ordinary differential equation x2d2ydx2-3xdydx+3y=0, x>0 with y(x) as a general solution. Given that y(1)=1 and y(2)=14, the…
- GATE 2020 EC Q14 – The general solution of d2ydx2-6dydx+9y=0 is
- GATE 2020 EC Q37 – Which one of the following options contains two solutions of the differential equation dydx=(y-1)x?
- GATE 2021 EC Q12 – Consider the differential equation given below. dydx+x1-x2\,y=x y The integrating factor of the differential equation is
- GATE 2022 EC Q25 – Consider the following partial differential equation (PDE) a2f(x,y) x2+b2f(x,y) y2=f(x,y), where a and b are distinct positive real numbers. Select…
- GATE 2024 EC Q11 – The general form of the complementary function of a differential equation is given by y(t)=(At+B)e-2t, where A and B are real constants determined by…
- GATE 2025 EC Q32 – The function y(t) satisfies t2y''(t)-2ty'(t)+2y(t)=0, where y'(t) and y''(t) denote the first and second derivatives of y(t), respectively. Given…
- GATE 2026 EC Q11 – Consider the differential equation w = Aw, with w(t=0) = bmatrix1\\1bmatrix. If w(t) = etu x + e-2tu y be the solution to the equation where u x and u…