1
GATE EE 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
$$x = {t \over 2}$$
2
GATE EE 2011
+1
-0.3
With $$K$$ as constant, the possible solution for the first order differential equation $${{dy} \over {dx}} = {e^{ - 3x}}$$ is
A
$${{ - 1} \over 3}{e^{ - 3x}} + K$$
B
$${1 \over 3}\left( { - 1} \right){e^{ 3x}} + K$$
C
$$- 3{e^{ - 3x}} + K$$
D
$$- 3{e^{ - x}} + K$$
3
GATE EE 2005
+1
-0.3
The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \right),\,x\left( 0 \right) = {x_0}\,\,\,\,$$ is
A
$$x\left( t \right) = {x_0}\,{e^{ - 3\,t}}$$
B
$$x\left( t \right) = {x_0}\,{e^{ - 3\,}}$$
C
$$x\left( t \right) = {x_0}\,{e^{ - t\,3}}$$
D
$$x\left( t \right) = {x_0}\,{e^{ - t\,}}$$
4
GATE EE 1995
+1
-0.3
If at every point of a certain curve , the slope of the tangent equals $${{ - 2x} \over y},$$ the curve is _______.
A
A straight line
B
A parabola
C
A circle
D
An Ellipse
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