GATE ME 2014 Set 1 | Differential Equations Question 15 | Engineering Mathematics

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.6

The matrix form of the linear system $${{dx} \over {dt}} = 3x - 5y$$ and $$\,{{dy} \over {dt}} = 4x + 8y\,\,$$ is

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & { - 5} \cr 4 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 3 & 8 \cr 4 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & { - 5} \cr 3 & 8 \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

$${d \over {dt}}\left\{ {\matrix{ x \cr y \cr } } \right\} = \left[ {\matrix{ 4 & 8 \cr 3 & { - 5} \cr } } \right]\left\{ {\matrix{ x \cr y \cr } } \right\}$$

GATE ME 2013

MCQ (Single Correct Answer)

-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

$$u = U{x \over L}$$

$$u = U\left( {{{1 - {e^{kx}}} \over {1 - {e^{kL}}}}} \right)$$

$$u = U\left( {{{1 - {e^{ - kx}}} \over {1 - {e^{ - kL}}}}} \right)$$

$$u = U\left( {{{1 + {e^{kx}}} \over {1 + {e^{kL}}}}} \right)$$

GATE ME 2012

MCQ (Single Correct Answer)

-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

$${x^2}$$

$$\sin \left( {{{\pi x} \over 2}} \right)$$

$${e^x}\sin \left( {{{\pi x} \over 2}} \right)$$

$${e^{ - x}}\sin \left( {{{\pi x} \over 2}} \right)$$

GATE ME 2008

MCQ (Single Correct Answer)

-0.6

It is given that $$y'' + 2y' + y = 0,\,\,\,\,y\left( 0 \right) = 0,y\left( 1 \right) = 0.$$ What is $$y(0.5)$$?

$$0$$

$$0.37$$

$$0.62$$

$$1.13$$