1
GATE ME 2014 Set 1
+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
$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & 8 \cr 3 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$
2
GATE ME 2014 Set 1
Numerical
+2
-0
If $$\,y = f\left( x \right)\,\,$$ is the solution of $${{{d^2}y} \over {d{x^2}}} = 0$$ with the boundary conditions $$y=5$$ at $$x=0,$$ and $$\,{{dy} \over {dx}} = 2$$ at $$x=10,$$ $$f(15)=$$_______.
3
GATE ME 2013
+2
-0.6
The solution to the differential equation $$\,{{{d^2}u} \over {d{x^2}}} - k{{du} \over {dx}} = 0\,\,\,$$ where $$'k'$$ is a constant, subjected to the boundary conditions $$\,\,u\left( 0 \right) = 0\,\,$$ and $$\,\,\,u\left( L \right) = U,\,\,$$ is
A
$$u = U{x \over L}$$
B
$$u = U\left( {{{1 - {e^{kx}}} \over {1 - {e^{kL}}}}} \right)$$
C
$$u = U\left( {{{1 - {e^{ - kx}}} \over {1 - {e^{ - kL}}}}} \right)$$
D
$$u = U\left( {{{1 + {e^{kx}}} \over {1 + {e^{kL}}}}} \right)$$
4
GATE ME 2012
+2
-0.6
Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ and $$\,\,y\left( 1 \right) = 1.\,\,\,$$ The complete solution of the differential equation is
A
$${x^2}$$
B
$$\sin \left( {{{\pi x} \over 2}} \right)$$
C
$${e^x}\sin \left( {{{\pi x} \over 2}} \right)$$
D
$${e^{ - x}}\sin \left( {{{\pi x} \over 2}} \right)$$
GATE ME Subjects
EXAM MAP
Medical
NEET