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GATE ECE
Differential Equations
Engineering Mathematics
Previous Years Questions
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Marks 1
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Consider the following partial differential equation (PDE) $$a{{{\partial ^2}f(x,y)} \over {\partial {x^2}}} + b{{{\part...
GATE ECE 2022
GO TO QUESTION
The general solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} - 5y = 0\,\,\,$$ ...
GATE ECE 2017 Set 2
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Consider the following statements about the linear dependence of the real valued functions $${y_1} = 1,\,\,{y_2} = x$$ a...
GATE ECE 2017 Set 1
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Consider the differential equation $$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$ with initial condition $$x(0)=1.$$ The respo...
GATE ECE 2015 Set 2
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The general solution of the differential equation $$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$ i...
GATE ECE 2015 Set 2
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If $$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
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If the characteristic equation of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} + ...
GATE ECE 2014 Set 2
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With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\...
GATE ECE 2012
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The solution of differential equation $${{dy} \over {dx}} = ky,y\left( 0 \right) = C$$ is
GATE ECE 2011
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The order of differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{dy} \over {dx}}} \right)^3} + {y^4} = {e...
GATE ECE 2009
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A solution of the differential equation $${{{d^2}y} \over {d{x^2}}} - 5{{dy} \over {dx}} + 6y = 0\,$$ is given by
GATE ECE 2005
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The following differential equation has $$3{{{d^2}y} \over {d{t^2}}} + 4{\left( {{{dy} \over {dt}}} \right)^3} + {y^2} +...
GATE ECE 2005
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$$y = {e^{ - 2x}}$$ is a solution of the differential equation $$\,{y^{11}} + {y^1} - 2y = 0$$
GATE ECE 1994
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Marks 2
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A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation $${{dy} \over {dx}} = {{...
GATE ECE 2018
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The position of a particle y(t) is described by the differential equation : $${{{d^2}y} \over {d{t^2}}} = - {{dy} \over...
GATE ECE 2018
GO TO QUESTION
Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left...
GATE ECE 2017 Set 1
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The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}...
GATE ECE 2016 Set 3
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The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\le...
GATE ECE 2015 Set 1
GO TO QUESTION
Consider the differential equation $${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x...
GATE ECE 2015 Set 3
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Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independe...
GATE ECE 2014 Set 3
GO TO QUESTION
With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equati...
GATE ECE 2014 Set 4
GO TO QUESTION
A function $$n(x)$$ satisfies the differential equation $${{{d^2}n\left( x \right)} \over {d{x^2}}} - {{n\left( x \right...
GATE ECE 2010
GO TO QUESTION
Match each differential equation in Group $$I$$ to its family of solution curves from Group $$II.$$ Group $$I$$ $$P:$...
GATE ECE 2009
GO TO QUESTION
Which of the following is a solution to the differential equation $${d \over {dt}}x\left( t \right) + 3x\left( t \right)...
GATE ECE 2008
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The solution of the differential equation $${k^2}{{{d^2}y} \over {d\,{x^2}}} = y - {y_2}\,\,$$ under the boundary condi...
GATE ECE 2007
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For the differential equation $${{{d^2}y} \over {d{x^2}}} + {k^2}y = 0,$$ the boundary conditions are (i) $$y=0$$ fo...
GATE ECE 2006
GO TO QUESTION
Solve the differential equation $${{{d^2}y} \over {d{x^2}}} + y = x\,\,$$ with the following conditions $$(i)$$ at $$x=...
GATE ECE 2001
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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
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