GATE Questions & Answers of Differential equations Electronics and Communication Engg

Which one of the following is a property of the solutions to the Laplace equation: $ \nabla^2f=0? $

The ordinary differential equation

$\frac{dx}{dt}=-3x+2,$ with $ \mathrm x\left(0\right)=1 $

is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is ________

The particular solution of the initial value problem given below is

$ \frac{d^2y}{dx^2}+12\frac{dy}{dx}+36y=0\;\; $ with $y\left(0\right)=3$ and $ \frac{dy}{dx}\vert_{x=0}=-36 $

The solution of the differential equation d2ydt2+2dydt+y=0 with $ y(0)=y'(0)=1 $ is

The general solution of the differential equation dydx=1+cos2y1-cos2x is

Consider the differential equation

d2xtdt2+3dxtdt+2xt=0

Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _____.

If the characteristic equation of the differential equation

d2ydx2+2αdydx+y=0

has two equal roots, then the values of α are

Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

If a and b are constants, the most general solution of the differential equation

d2xdt2+2dxdt+x=0 is

With initial values y(0)=y′(0)=1, the solution of the differential equation

d2ydx2+4dydx+4y=0

at x=1 is _____.

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t > 0 , when the forcing function is x(t) and the initial condition is y(0) . If one wishes to modify the system so that the solution becomes -2y(t) for t > 0 , we need to

With initial condition x(1)=0.5 , the solution of the differential equation,

tdxdt+x=t is

Consider the differential equation

d2ytdt2+2dytdt+yt=δt with y(t)t=0-=-2 and dydtt=0-=0

The numerical value of dydtt=0+ is

(A) –2 (B) –1 (C) 0 (D) 1

The solution of the differential equation dydx=ky,y0=c is

A function n(x) satisfied the differential equation d2nxdx2-nxL2=0 where L is a constant. The boundary conditions are: n(0)=K and n ( ∞ ) = 0. The solution to this equation is

Consider differential equation dy(x)dx-yx=x with the initial condition y(0) = 0. Using Euler’s first order method with a step size of 0.1, the value of y (0.3) is

The order of the differential equation d2ydt2+dydt3+y4=e-t is

Match each differential equation in Group I to its family of solution curves from Group II.

  Group I   Group II
P. dydx=yx 1. Circles
Q. dydx=-yx 2. Straight lines
R. dydx=xy 3. Hyperbolas
S. dydx=-xy    

Which of the following is a solution to the differential equation dxtdt+3xt=0 ?

The solution of the differential equation k2d2ydx2=y-y2 under the boundary conditions (i) y = y1 at x = 0 and (ii) y = y2 at x = , where k, y1 and y2 are constants, is