1
GATE ECE 2015 Set 3
Numerical
+2
-0
Consider the differential equation $${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x\left( t \right) = 0$$
Given $$x(0) = 20$$ & $$\,x\left( 1 \right) = {{10} \over e},$$ where $$e=2.718,$$

The value of $$x(2)$$ is

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2
GATE ECE 2015 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\left( 0 \right) = {y^1}\left( 0 \right) = 1\,\,$$ is
A
$$\left( {2 - t} \right){e^t}$$
B
$$\left( {1 + 2t} \right){e^{ - t}}$$
C
$$\left( {2 + t} \right){e^{ - t}}$$
D
$$\left( {1 - 2t} \right){e^t}$$
3
GATE ECE 2014 Set 4
Numerical
+2
-0
With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y = 0\,\,$$ at $$x=1$$ is ________.
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4
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independent and dependent variables respectively?
A
$${{dy} \over {dx}} + xy = {e^{ - x}}$$
B
$${{dy} \over {dx}} + xy = 0$$
C
$${{dy} \over {dx}} + xy = {e^{ - y}}$$
D
$${{dy} \over {dx}} + {e^{ - y}} = 0$$
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