1
GATE ECE 2014 Set 4
+1
-0.3
If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{{dx} \over {dt}} + x = 0$$ is
A
$$a{e^{ - t}}$$
B
$$a{e^{ - t}} + bt{e^{ - t}}$$
C
$$a{e^t} + bt{e^{ - t}}$$
D
$$a{e^{ - 2t}}$$
2
GATE ECE 2014 Set 2
+1
-0.3
If the characteristic equation of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 2\alpha {{dy} \over {dx}} + y = 0\,\,$$ has two equal roots, then the values of $$\alpha$$ are
A
$$\pm \,\,1$$
B
$$0,0$$
C
$$\pm \,\,j$$
D
$$\pm \,\,1/2$$
3
GATE ECE 2012
+1
-0.3
With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is
A
$$x = t - {1 \over 2}$$
B
$$x = {t^2} - {1 \over 2}$$
C
$$xt = {{{t^2}} \over 2}$$
D
$$x = {t \over 2}$$
4
GATE ECE 2011
+1
-0.3
The solution of differential equation $${{dy} \over {dx}} = ky,y\left( 0 \right) = C$$ is
A
$$x = C{e^{ky}}$$
B
$$x = k{e^{Cy}}$$
C
$$y = {e^{kx}}C$$
D
$$y = C{e^{ - kx}}$$
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