GATE EE
Engineering Mathematics
Differential Equations
Previous Years Questions

## Marks 1

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\... With$$K$$as constant, the possible solution for the first order differential equation$${{dy} \over {dx}} = {e^{ - 3x}}$$is The solution of the first order differential equation$$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \right),\,x\left( 0 \right) = {x...
If at every point of a certain curve , the slope of the tangent equals $${{ - 2x} \over y},$$ the curve is _______.

## Marks 2

Consider the differential equation $$\left( {{t^2} - 81} \right){{dy} \over {dt}} + 5ty = \sin \left( t \right)\,\,$$ with $$y\left( 1 \right) = 2\pi... Let$$y(x)$$be the solution of the differential equation$$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y = 0\,\,$$with initial conditions ... A function$$y(t),$$such that$$y(0)=1$$and$$\,y\left( 1 \right) = 3{e^{ - 1}},\,\,$$is a solution of the differential equation$$\,\,{{{d^2}y} \...
A solution of the ordinary differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y = 0\,\,$$ is such that $$y(0)=2$$ and $$y(... A differential equation$$\,\,{{di} \over {dt}} - 0.21 = 0\,\,$$is applicable over$$\,\, - 10 < t < 10.\,\,$$If$$i(4)=10,$$then$$i(-5)$$... The solution for the differential equation$$\,\,{{{d^2}x} \over {d{t^2}}} = - 9x,\,\,$$with initial conditions$$x(0)=1$$and$${{{\left. {\,\,\,...
Consider the differential equation $${x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - y = 0.\,\,$$ Which of the following is a solution to this ...
For the differential equation $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 8x = 0$$ with initial conditions $$x(0)=1$$ and $${\left( {{{dx} \o... For the equation$$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \right) + 2x\left( t \right) = 5,...
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