1
GATE ECE 2017 Set 1
+2
-0.6
Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left( {x + y - 1} \right)^2}$$ , where $$x,$$ $$y$$ are real ?
A
$$y = 1 + x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant
B
$$y = 1 + x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant
C
$$y = 1 - x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant
D
$$y = 1 - x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant
2
GATE ECE 2016 Set 3
+2
-0.6
The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}} + 36y = 0\,\,$$ with $$\,y\left( 0 \right) = 3\,\,$$ and $$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 0}} = - 36\,\,$$
A
$$\left( {3 - 18x} \right){e^{ - 6x}}$$
B
$$\left( {3 + 25x} \right){e^{ - 6x}}$$
C
$$\left( {3 + 20x} \right){e^{ - 6x}}$$
D
$$\left( {3 - 12x} \right){e^{ - 6x}}$$
3
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

4
GATE ECE 2015 Set 1
+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
$$\left( {1 - 2t} \right){e^t}$$
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
EXAM MAP
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