1
GATE EE 2014 Set 2
+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
+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
+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
+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
$$10$$
EXAM MAP
Medical
NEET