1
GATE PI 2010
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$
A
$${{dy} \over {dx}} - {5 \over 3}\cos \left( {3x} \right) = 0$$
B
$${{dy} \over {dx}} + {5 \over 3}\left( {\cos 3x} \right) = 0$$
C
$${{{d^2}y} \over {{d^2}\,x}} + 9y = 0$$
D
$${{{d^2}y} \over {d{x^2}}} - 9y = 0$$
2
GATE PI 2009
MCQ (Single Correct Answer)
+2
-0.6
The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions
(i) $${{dy} \over {dx}} = 1$$ at $$x=0$$
(ii) $${{dy} \over {dx}} = 1$$ at $$x=1$$
A
$$y=1$$
B
$$y=x$$
C
$$y=x+c$$ where $$c$$ is an arbitrary constant.
D
$$\,y = {C_1}x + {C_2}$$ where $${C_1},\,{C_2}$$ are arbitrary constants
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