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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},$$the curve is _______. GATE EE 1995 ## Marks 2 More Consider the differential equation$$\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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