GATE CE

Differential Equations

Engineering Mathematics

(Past Years Questions)

Marks 1

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The solution of the equation $$\,{{dQ} \over {dt}} + Q = 1$$ with $$Q=0$$ at $$t=0$$ is
GATE CE 2017 Set 1
Consider the following partial differential equation: $$\,\,3{{{\partial ^2}\phi } \over {\partial {x^2}}} + B{{{\parti...
GATE CE 2017 Set 1
Consider the following second $$-$$order differential equation : $$\,y''\,\, - 4y' + 3y = 2t - 3{t^2}\,\,\,$$ The part...
GATE CE 2017 Set 1
The type of partial differential equation $${{{\partial ^2}p} \over {\partial {x^2}}} + {{{\partial ^2}p} \over {\parti...
GATE CE 2016 Set 1
The integrating factor for the differential equation $${{dP} \over {dt}} + {k_2}\,P = {k_1}{L_0}{e^{ - {k_1}t}}\,\,$$ i...
GATE CE 2014 Set 2
The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$...
GATE CE 2011
The order and degree of a differential equation $${{{d^3}y} \over {d{x^3}}} + 4\sqrt {{{\left( {{{dy} \over {dx}}} \righ...
GATE CE 2010
The partial differential equation that can be formed from $$z=ax+by+ab$$ has the form $$\,\,\left( {p = {{\partial z} \...
GATE CE 2010
Solution of the differential equation $$3y{{dy} \over {dx}} + 2x = 0$$ represents a family of
GATE CE 2009
The degree of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{x^3} = 0\,\,$$ is
GATE CE 2007
A body originally at $${60^ \circ }$$ cools down to $$40$$ in $$15$$ minutes when kept in air at a temperature of $${25^...
GATE CE 2007
The solution of the differential equation $$\,{x^2}{{dy} \over {dx}} + 2xy - x + 1 = 0\,\,\,$$ given that at $$x=1,$$ $...
GATE CE 2006
The number of boundary conditions required to solve the differential equation $$\,\,{{{\partial ^2}\phi } \over {\parti...
GATE CE 2001
If $$c$$ is a constant, then the solution of $${{dy} \over {dx}} = 1 + {y^2}$$ is
GATE CE 1999
For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is
GATE CE 1997
The differential equation $${y^{11}} + {\left( {{x^3}\,\sin x} \right)^5}{y^1} + y = \cos {x^3}\,\,\,\,$$ is
GATE CE 1995
The necessary & sufficient condition for the differential equation of the form $$\,\,M\left( {x,y} \right)dx + N\left( {...
GATE CE 1994

Marks 2

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The solution of the partial differential equation $${{\partial u} \over {\partial t}} = \alpha {{{\partial ^2}u} \over {...
GATE CE 2016 Set 1
Consider the following second order linear differential equation $${{{d^2}y} \over {d{x^2}}} = - 12{x^2} + 24x - 20$$ ...
GATE CE 2015 Set 2
Consider the following differential equation $$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$ $$\...
GATE CE 2015 Set 1
Water is following at a steady rate through a homogeneous and saturated horizontal soil strip of $$10$$m length. The str...
GATE CE 2014 Set 2
The solution of the ordinary differential equation $${{dy} \over {dx}} + 2y = 0$$ for the boundary condition, $$y=5$$ at...
GATE CE 2012
The solution to the ordinary differential equation $${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} - 6y = 0\,\,\,$$ is
GATE CE 2010
The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x...
GATE CE 2007
Transformation to linear form by substituting $$v = {y^{1 - n}}$$ of the equation $${{dy} \over {dt}} + p\left( t \righ...
GATE CE 2005
The solution $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 17y = 0;$$ $$y\left( 0 \right) = 1,{\left( {{{d\,y} \ov...
GATE CE 2005
Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equ...
GATE CE 2004
The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \righ...
GATE CE 2001
Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$
GATE CE 1998
The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,
GATE CE 1997
Solve $${{{d^4}v} \over {d{x^4}}} + 4{\lambda ^4}v = 1 + x + {x^2}$$
GATE CE 1996
The solution of a differential equation $${y^{11}} + 3{y^1} + 2y = 0$$ is of the form
GATE CE 1995
The differential equation $${{{d^4}y} \over {d{x^4}}} + P{{{d^2}y} \over {d{x^2}}} + ky = 0\,\,$$ is
GATE CE 1994

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