1
GATE ME 2017 Set 2
Numerical
+2
-0
Consider the differential equation $$\,\,3y''\left( x \right) + 27y\left( x \right) = 0\,\,$$ with initial conditions $$y\left( 0 \right) = 0$$ and $$y'\left( 0 \right) = 2000.\,\,$$ The value of $$y$$ at $$x=1$$ is __________.
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2
GATE ME 2016 Set 1
Numerical
+2
-0
If $$y = f(x)$$ satiesfies the boundary value problem $$\,\,y''\,\,\, + \,\,\,9y\,\,\, = \,\,\,0,\,\,\,y\left( 0 \right)\,\,\, = \,\,\,0,\,$$ $$\,\,y\left( {{\pi \over 2}} \right) = \sqrt 2 ,\,\,\,$$ then $$\,\,y\left( {{\pi \over 4}} \right)\,\,$$ is _______.
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3
GATE ME 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The general solution of the differential equation $$\,\,{{dy} \over {dx}} = \cos \left( {x + y} \right),\,\,$$ with $$c$$ as a constant, is
A
$$y + \sin \left( {x + y} \right) = x + c$$
B
$$\tan \left( {{{x + y} \over 2}} \right) = y + c$$
C
$$\cos \left( {{{x + y} \over 2}} \right) = x + c$$
D
$$\tan \left( {{{x + y} \over 2}} \right) = x + c$$
4
GATE ME 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The matrix form of the linear system $${{dx} \over {dt}} = 3x - 5y$$ and $$\,{{dy} \over {dt}} = 4x + 8y\,\,$$ is
A
$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & { - 5} \cr 4 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$
B
$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & 8 \cr 4 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$
C
$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & { - 5} \cr 3 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$
D
$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & 8 \cr 3 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$
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