GATE EE

Differential Equations

Engineering Mathematics

(Past Years Questions)

Marks 1

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With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\...
GATE EE 2012
With $$K$$ as constant, the possible solution for the first order differential equation $${{dy} \over {dx}} = {e^{ - 3x...
GATE EE 2011
The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \r...
GATE EE 2005
If at every point of a certain curve , the slope of the tangent equals $${{ - 2x} \over y},$$ the curve is _______.
GATE EE 1995

Marks 2

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Consider the differential equation $$\left( {{t^2} - 81} \right){{dy} \over {dt}} + 5ty = \sin \left( t \right)\,\,$$ w...
GATE EE 2017 Set 1
Let $$y(x)$$ be the solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y = 0\...
GATE EE 2016 Set 2
A function $$y(t),$$ such that $$y(0)=1$$ and $$\,y\left( 1 \right) = 3{e^{ - 1}},\,\,$$ is a solution of the differenti...
GATE EE 2016 Set 1
A differential equation $$\,\,{{di} \over {dt}} - 0.21 = 0\,\,$$ is applicable over $$\,\, - 10 ...
GATE EE 2015 Set 2
A solution of the ordinary differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y = 0\,\,$$ is...
GATE EE 2015 Set 1
Consider the differential equation $${x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - y = 0.\,\,$$ Which of the fo...
GATE EE 2014 Set 2
The solution for the differential equation $$\,\,{{{d^2}x} \over {d{t^2}}} = - 9x,\,\,$$ with initial conditions $$x(0...
GATE EE 2014 Set 1
For the differential equation $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 8x = 0$$ with initial conditions $$x(...
GATE EE 2010
For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \ri...
GATE EE 2005

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