1

GATE CE 2015 Set 1

MCQ (Single Correct Answer)

+2

-0.6

Consider the following differential equation

$$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$

$$\,\,\,\,\,\,\,\,\,\, = y\left( {x\,dy - y\,dx} \right)\sin \left( {{y \over x}} \right)$$

$$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$

$$\,\,\,\,\,\,\,\,\,\, = y\left( {x\,dy - y\,dx} \right)\sin \left( {{y \over x}} \right)$$

Which of the following is the solution of the above equation ($$C$$ is an arbitrary constant)

2

GATE CE 2015 Set 2

Numerical

+2

-0

Consider the following second order linear differential equation $${{{d^2}y} \over {d{x^2}}} = - 12{x^2} + 24x - 20$$

The boundary conditions are: at $$x=0, y=5$$ and at $$x=2, y=21$$

The value of $$y$$ at $$x=1$$ is

The boundary conditions are: at $$x=0, y=5$$ and at $$x=2, y=21$$

The value of $$y$$ at $$x=1$$ is

Your input ____

3

GATE CE 2014 Set 2

Numerical

+2

-0

Water is following at a steady rate through a homogeneous and saturated horizontal soil strip of $$10$$m length. The strip is being subjected to a constant water head $$(H)$$ of $$5$$m at the beginning and $$1$$m at the end. If the governing equation of flow in the soil strip is $$\,\,{{{d^2}H} \over {d{x^2}}} = 0\,\,$$ (where $$x$$ is the distance along the soil strip), the value of $$H$$ (in m) at the middle of the strip is _______.

Your input ____

4

GATE CE 2012

MCQ (Single Correct Answer)

+2

-0.6

The solution of the ordinary differential equation $${{dy} \over {dx}} + 2y = 0$$ for the boundary condition, $$y=5$$ at $$x=1$$ is

Questions Asked from Differential Equations (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CE 2024 Set 1 (1)
GATE CE 2016 Set 1 (1)
GATE CE 2015 Set 1 (1)
GATE CE 2015 Set 2 (1)
GATE CE 2014 Set 2 (1)
GATE CE 2012 (1)
GATE CE 2010 (1)
GATE CE 2007 (1)
GATE CE 2005 (2)
GATE CE 2004 (1)
GATE CE 2001 (1)
GATE CE 1998 (1)
GATE CE 1997 (1)
GATE CE 1996 (1)
GATE CE 1995 (1)
GATE CE 1994 (1)

GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude