GATE ECE

Differential Equations

Engineering Mathematics

(Past Years Questions)

Marks 1

More
The general solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} - 5y = 0\,\,\,$$ ...
GATE ECE 2017 Set 2
Consider the following statements about the linear dependence of the real valued functions $${y_1} = 1,\,\,{y_2} = x$$ a...
GATE ECE 2017 Set 1
The general solution of the differential equation $$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$ i...
GATE ECE 2015 Set 2
Consider the differential equation $$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$ with initial condition $$x(0)=1.$$ The respo...
GATE ECE 2015 Set 2
If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} ...
GATE ECE 2014 Set 4
If the characteristic equation of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} + ...
GATE ECE 2014 Set 2
With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\...
GATE ECE 2012
The solution of differential equation $${{dy} \over {dx}} = ky,y\left( 0 \right) = C$$ is
GATE ECE 2011
The order of differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{dy} \over {dx}}} \right)^3} + {y^4} = {e...
GATE ECE 2009
The following differential equation has $$3{{{d^2}y} \over {d{t^2}}} + 4{\left( {{{dy} \over {dt}}} \right)^3} + {y^2} +...
GATE ECE 2005
A solution of the differential equation $${{{d^2}y} \over {d{x^2}}} - 5{{dy} \over {dx}} + 6y = 0\,$$ is given by
GATE ECE 2005
$$y = {e^{ - 2x}}$$ is a solution of the differential equation $$\,{y^{11}} + {y^1} - 2y = 0$$
GATE ECE 1994

Marks 2

More
The position of a particle y(t) is described by the differential equation : $${{{d^2}y} \over {d{t^2}}} = - {{dy} \over...
GATE ECE 2018
A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation $${{dy} \over {dx}} = {{...
GATE ECE 2018
Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left...
GATE ECE 2017 Set 1
The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}...
GATE ECE 2016 Set 3
Consider the differential equation $${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x...
GATE ECE 2015 Set 3
The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\le...
GATE ECE 2015 Set 1
With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equati...
GATE ECE 2014 Set 4
Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independe...
GATE ECE 2014 Set 3
A function $$n(x)$$ satisfies the differential equation $${{{d^2}n\left( x \right)} \over {d{x^2}}} - {{n\left( x \right...
GATE ECE 2010
Match each differential equation in Group $$I$$ to its family of solution curves from Group $$II.$$ Group $$I$$ $$P:$...
GATE ECE 2009
Which of the following is a solution to the differential equation $${d \over {dt}}x\left( t \right) + 3x\left( t \right)...
GATE ECE 2008
The solution of the differential equation $${k^2}{{{d^2}y} \over {d\,{x^2}}} = y - {y_2}\,\,$$ under the boundary condi...
GATE ECE 2007
For the differential equation $${{{d^2}y} \over {d{x^2}}} + {k^2}y = 0,$$ the boundary conditions are (i) $$y=0$$ fo...
GATE ECE 2006
Solve the differential equation $${{{d^2}y} \over {d{x^2}}} + y = x\,\,$$ with the following conditions $$(i)$$ at $$x=...
GATE ECE 2001
Match each of the items $$A, B, C$$ with an appropriate item from $$1, 2, 3, 4$$ and $$5$$ List-$${\rm I}$$ $$(P)$$ $${a...
GATE ECE 1994

EXAM MAP

Graduate Aptitude Test in Engineering

GATE ECE GATE CSE GATE CE GATE EE GATE ME GATE PI GATE IN

Joint Entrance Examination

JEE Main JEE Advanced