1
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
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 differential equation for $$x > 0?$$
A
$${e^x}$$
B
$${x^2}$$
C
$$1/x$$
D
$$lnx$$
2
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The solution for the differential equation $$\,\,{{{d^2}x} \over {d{t^2}}} = - 9x,\,\,$$ with initial conditions $$x(0)=1$$ and $${{{\left. {\,\,\,\,{{dx} \over {dt}}} \right|}_{t = 0}} = 1,\,\,}$$ is
A
$${t^2} + t + 1$$
B
$$\sin 3t + {1 \over 3}\cos 3t + {2 \over 3}$$
C
$${1 \over 3}\sin 3t + \cos 3t$$
D
$$\cos 3t + t$$
3
GATE EE 2010
MCQ (Single Correct Answer)
+2
-0.6
For the differential equation $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 8x = 0$$ with initial conditions $$x(0)=1$$ and $${\left( {{{dx} \over {dt}}} \right)_{t = 0}}$$ $$=0$$ the solution
A
$$x\left( t \right) = 2{e^{ - 6t}} - {e^{ - 2t}}$$
B
$$x\left( t \right) = 2{e^{ - 2t}} - {e^{ - 4t}}$$
C
$$x\left( t \right) = - {e^{ - 6t}} - 2{e^{ - 4t}}$$
D
$$x\left( t \right) = - {e^{ - 2t}} - 2{e^{ - 4t}}$$
4
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \right) + 2x\left( t \right) = 5,\,\,\,$$ the solution $$x(t)$$ approaches the following values as $$t \to \infty $$
A
$$0$$
B
$$5/2$$
C
$$5$$
D
$$10$$
GATE EE Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12