GATE Questions & Answers of Differential equations Civil Engineering

The Laplace transform $ F(s) $ of the exponential function, $ f(t)=e^{at} $ when  $ t\geq0 $ , where a is a constant and $ (s-a)>0 $ , is

Consider the following partial differential equation:

$\style{font-family:'Times New Roman'}{3\frac{\partial^2\phi}{\partial x^2}+B\frac{\partial^2\phi}{\partial x\partial y}+3\frac{\partial^2\phi}{\partial y^2}+4\phi=0}$

For this equation to be classified as parabolic , the value of B2 must be _____________.

The solution of the equation $\style{font-family:'Times New Roman'}{\frac{dQ}{dt}+Q=1}$ with Q = 0 at t = 0

Consider the following second-order differential equation:

$\style{font-family:'Times New Roman'}{y''-4y'+3y=2t-3t^2}$

The particular solution of the differential equation is

The type of partial differential equation 2Px2+2Py2+32Pxy+2Px-Py=0 is

The solution of the partial differential equation ut=α2ux2 is of the form

The respective expressions for complimentary function and particular integral part of the solution of the differential equation d4ydx4+3d2ydx2=108x2 are

Consider the following differential equation:

$ \mathrm x(\mathrm{ydx}+\mathrm{xdy})\cos\frac{\mathrm y}{\mathrm x}=\mathrm y(\mathrm{xdy}-\mathrm{ydx})\sin\frac{\mathrm y}{\mathrm x} $

Which of the following is the solution of the above equation (c is an arbitrary constant) ?

Consider the following second order linear differential equation

d2ydx2=-12x2+24x-20

The boundary conditions are : at $ x=0,y=5 $ and at $ x=2,y=21 $
The value of $ y $ at $ x=1 $ is ___________

The integrating factor for the differential equation dpdt+k2P=k1Loe-k1t is

The solution of the ordinary differential equation dydx+2y=0 for the boundary condition, y = 5 at x = 1 is

The solution of the differential equation dydx+yx=x , with the condition that y=1 at x=1, is

The order and degree of the differential equation

d3ydx3+4dydx3+y2=0 are respectively

The solution to the ordinary differential equation

d2ydx2+dydx-6y=0 is

The partial differential equation that can be formed from

z = ax + by + ab has the form with p=zx and q=zy

A parabolic cable is held between two supports at the same level. They horizontal span between the supports is L. The sag at the mid-span is h. The equation of the parabola is y = 4hx2L2, where x is the horizontal coordinate and y is the L vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is

Solution of the differential equation 3ydydx+2x=0represents a family of

Laplace transform for the function fx=coshax is

The general solution of d2ydx2+y=0 is

The equation kx2hx2+kz2hz2=0 can be transformed to 2hxt2+2hz2=0 by substituting

Solution of dydx=-xy at x = 1 and y = 3 is

The degree of the differential equation d2xdt2+2x3=0 is

The solution for the differential equation dydx=x2y with the condition that y = 1 at x = 0 is

A body originally at 60°C cools down to 40°C in 15 minutes when kept in air at a temperature of 25°C. What will be the temperature of the body at the end of 30 minutes?