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## Marks 1

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Consider the following partial differential equation (PDE) $$a{{{\partial ^2}f(x,y)} \over {\partial {x^2}}} + b{{{\part... GATE ECE 2022 The general solution of the differential equation$$\,\,{{{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$$a... GATE ECE 2017 Set 1 Consider the differential equation$$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$with initial condition$$x(0)=1.$$The respo... GATE ECE 2015 Set 2 The general solution of the differential equation$$\,\,{{dy} \over {dx}} = {{1 + \cos 2y} \over {1 - \cos 2x}}\,\,$$i... GATE ECE 2015 Set 2 If$$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 $$\,\,{{{d^2}y} \over {d{t^2}}} + {\left( {{{dy} \over {dx}}} \right)^3} + {y^4} = {e... GATE ECE 2009 A solution of the differential equation$${{{d^2}y} \over {d{x^2}}} - 5{{dy} \over {dx}} + 6y = 0\,$$is given by GATE ECE 2005 The following differential equation has$$3{{{d^2}y} \over {d{t^2}}} + 4{\left( {{{dy} \over {dt}}} \right)^3} + {y^2} +...
GATE ECE 2005
$$y = {e^{ - 2x}}$$ is a solution of the differential equation $$\,{y^{11}} + {y^1} - 2y = 0$$
GATE ECE 1994

## Marks 2

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A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation $${{dy} \over {dx}} = {{... GATE ECE 2018 The position of a particle y(t) is described by the differential equation :$${{{d^2}y} \over {d{t^2}}} = - {{dy} \over...
GATE ECE 2018
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
The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\le... GATE ECE 2015 Set 1 Consider the differential equation$${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x...
GATE ECE 2015 Set 3
Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independe...
GATE ECE 2014 Set 3
With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equati...
GATE ECE 2014 Set 4
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.$$Group$$IP:$... 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

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